<!DOCTYPE html>
<html lang="en">
  <head>
    <title>BigInt Structure Reference</title>
    <link rel="stylesheet" type="text/css" href="../css/jazzy.css" />
    <link rel="stylesheet" type="text/css" href="../css/highlight.css" />
    <meta charset="utf-8">
    <script src="../js/jquery.min.js" defer></script>
    <script src="../js/jazzy.js" defer></script>
    
    <script src="../js/lunr.min.js" defer></script>
    <script src="../js/typeahead.jquery.js" defer></script>
    <script src="../js/jazzy.search.js" defer></script>
  </head>
  <body>

    <a name="//apple_ref/swift/Struct/BigInt" class="dashAnchor"></a>

    <a title="BigInt Structure Reference"></a>

    <header class="header">
      <p class="header-col header-col--primary">
        <a class="header-link" href="../index.html">
          BigInt v5.2.1 Docs
        </a>
         (85% documented)
      </p>
    
      <p class="header-col--secondary">
        <form role="search" action="../search.json">
          <input type="text" placeholder="Search documentation" data-typeahead>
        </form>
      </p>
    
        <p class="header-col header-col--secondary">
          <a class="header-link" href="https://github.com/attaswift/BigInt">
            <img class="header-icon" src="../img/gh.png"/>
            View on GitHub
          </a>
        </p>
    
        <p class="header-col header-col--secondary">
          <a class="header-link" href="dash-feed://https%3A%2F%2Fattaswift.github.io%2FBigInt%2Freference%2Fdocsets%2FBigInt.xml">
            <img class="header-icon" src="../img/dash.png"/>
            Install in Dash
          </a>
        </p>
    </header>

    <p class="breadcrumbs">
      <a class="breadcrumb" href="../index.html">BigInt Reference</a>
      <img class="carat" src="../img/carat.png" />
      BigInt Structure Reference
    </p>

    <div class="content-wrapper">
      <nav class="navigation">
        <ul class="nav-groups">
          <li class="nav-group-name">
            <a class="nav-group-name-link" href="../Extensions.html">Extensions</a>
            <ul class="nav-group-tasks">
              <li class="nav-group-task">
                <a class="nav-group-task-link" href="../Extensions/BinaryFloatingPoint.html">BinaryFloatingPoint</a>
              </li>
              <li class="nav-group-task">
                <a class="nav-group-task-link" href="../Extensions/String.html">String</a>
              </li>
            </ul>
          </li>
          <li class="nav-group-name">
            <a class="nav-group-name-link" href="../Structs.html">Structures</a>
            <ul class="nav-group-tasks">
              <li class="nav-group-task">
                <a class="nav-group-task-link" href="../Structs/BigInt.html">BigInt</a>
              </li>
              <li class="nav-group-task">
                <a class="nav-group-task-link" href="../Structs/BigInt/Sign.html">– Sign</a>
              </li>
              <li class="nav-group-task">
                <a class="nav-group-task-link" href="../Structs/BigInt/Words.html">– Words</a>
              </li>
              <li class="nav-group-task">
                <a class="nav-group-task-link" href="../Structs/BigUInt.html">BigUInt</a>
              </li>
              <li class="nav-group-task">
                <a class="nav-group-task-link" href="../Structs/BigUInt/Words.html">– Words</a>
              </li>
            </ul>
          </li>
        </ul>
      </nav>
      <article class="main-content">

        <section class="section">
          <div class="section-content top-matter">
            <h1>BigInt</h1>
              <div class="declaration">
                <div class="language">
                  
                  <pre class="highlight swift"><code><span class="kd">public</span> <span class="kd">struct</span> <span class="kt">BigInt</span> <span class="p">:</span> <span class="kt">SignedInteger</span></code></pre>
<pre class="highlight swift"><code><span class="kd">extension</span> <span class="kt">BigInt</span><span class="p">:</span> <span class="kt">Codable</span></code></pre>
<pre class="highlight swift"><code><span class="kd">extension</span> <span class="kt">BigInt</span><span class="p">:</span> <span class="kt">Hashable</span></code></pre>
<pre class="highlight swift"><code><span class="kd">extension</span> <span class="kt">BigInt</span><span class="p">:</span> <span class="kt">ExpressibleByIntegerLiteral</span></code></pre>
<pre class="highlight swift"><code><span class="kd">extension</span> <span class="kt">BigInt</span><span class="p">:</span> <span class="kt">Strideable</span></code></pre>
<pre class="highlight swift"><code><span class="kd">extension</span> <span class="kt">BigInt</span><span class="p">:</span> <span class="kt">ExpressibleByStringLiteral</span></code></pre>
<pre class="highlight swift"><code><span class="kd">extension</span> <span class="kt">BigInt</span><span class="p">:</span> <span class="kt">CustomStringConvertible</span></code></pre>
<pre class="highlight swift"><code><span class="kd">extension</span> <span class="kt">BigInt</span><span class="p">:</span> <span class="kt">CustomPlaygroundDisplayConvertible</span></code></pre>

                </div>
              </div>
            <p>An arbitary precision signed integer type, also known as a &ldquo;big integer&rdquo;.</p>

<p>Operations on big integers never overflow, but they might take a long time to execute.
The amount of memory (and address space) available is the only constraint to the magnitude of these numbers.</p>

<p>This particular big integer type uses base-2^64 digits to represent integers.</p>

<p><code>BigInt</code> is essentially a tiny wrapper that extends <code><a href="../Structs/BigUInt.html">BigUInt</a></code> with a sign bit and provides signed integer
operations. Both the underlying absolute value and the negative/positive flag are available as read-write 
properties.</p>

<p>Not all algorithms of <code><a href="../Structs/BigUInt.html">BigUInt</a></code> are available for <code>BigInt</code> values; for example, there is no square root or
primality test for signed integers. When you need to call one of these, just extract the absolute value:</p>
<pre class="highlight plaintext"><code>BigInt(255).abs.isPrime()   // Returns false
</code></pre>

              <div class="slightly-smaller">
                <a href="https://github.com/attaswift/tree/v5.2.1/Sources/BigInt.swift#L29-L74">Show on GitHub</a>
              </div>
          </div>
        </section>

        <section class="section">
          <div class="section-content">
            <div class="task-group">
              <ul class="item-container">
                <li class="item">
                  <div>
                    <code>
                    <a name="/s:6BigIntAAV4SignO"></a>
                    <a name="//apple_ref/swift/Enum/Sign" class="dashAnchor"></a>
                    <a class="token" href="#/s:6BigIntAAV4SignO">Sign</a>
                    </code>
                  </div>
                  <div class="height-container">
                    <div class="pointer-container"></div>
                    <section class="section">
                      <div class="pointer"></div>
                      <div class="abstract">
                        <p>Undocumented</p>

                        <a href="../Structs/BigInt/Sign.html" class="slightly-smaller">See more</a>
                      </div>
                      <div class="declaration">
                        <h4>Declaration</h4>
                        <div class="language">
                          <p class="aside-title">Swift</p>
                          <pre class="highlight swift"><code><span class="kd">public</span> <span class="kd">enum</span> <span class="kt">Sign</span></code></pre>

                        </div>
                      </div>
                      <div class="slightly-smaller">
                        <a href="https://github.com/attaswift/tree/v5.2.1/Sources/BigInt.swift#L30-L33">Show on GitHub</a>
                      </div>
                    </section>
                  </div>
                </li>
                <li class="item">
                  <div>
                    <code>
                    <a name="/s:Sj9MagnitudeQa"></a>
                    <a name="//apple_ref/swift/Alias/Magnitude" class="dashAnchor"></a>
                    <a class="token" href="#/s:Sj9MagnitudeQa">Magnitude</a>
                    </code>
                  </div>
                  <div class="height-container">
                    <div class="pointer-container"></div>
                    <section class="section">
                      <div class="pointer"></div>
                      <div class="abstract">
                        
                      </div>
                      <div class="declaration">
                        <h4>Declaration</h4>
                        <div class="language">
                          <p class="aside-title">Swift</p>
                          <pre class="highlight swift"><code><span class="kd">public</span> <span class="kd">typealias</span> <span class="kt">Magnitude</span> <span class="o">=</span> <span class="kt"><a href="../Structs/BigUInt.html">BigUInt</a></span></code></pre>

                        </div>
                      </div>
                      <div class="slightly-smaller">
                        <a href="https://github.com/attaswift/tree/v5.2.1/Sources/BigInt.swift#L">Show on GitHub</a>
                      </div>
                    </section>
                  </div>
                </li>
                <li class="item">
                  <div>
                    <code>
                    <a name="/s:6BigIntAAV4Worda"></a>
                    <a name="//apple_ref/swift/Alias/Word" class="dashAnchor"></a>
                    <a class="token" href="#/s:6BigIntAAV4Worda">Word</a>
                    </code>
                  </div>
                  <div class="height-container">
                    <div class="pointer-container"></div>
                    <section class="section">
                      <div class="pointer"></div>
                      <div class="abstract">
                        <p>The type representing a digit in <code>BigInt</code>&lsquo;s underlying number system.</p>

                      </div>
                      <div class="declaration">
                        <h4>Declaration</h4>
                        <div class="language">
                          <p class="aside-title">Swift</p>
                          <pre class="highlight swift"><code><span class="kd">public</span> <span class="kd">typealias</span> <span class="kt">Word</span> <span class="o">=</span> <span class="kt"><a href="../Structs/BigUInt.html">BigUInt</a></span><span class="o">.</span><span class="kt">Word</span></code></pre>

                        </div>
                      </div>
                      <div class="slightly-smaller">
                        <a href="https://github.com/attaswift/tree/v5.2.1/Sources/BigInt.swift#L38">Show on GitHub</a>
                      </div>
                    </section>
                  </div>
                </li>
                <li class="item">
                  <div>
                    <code>
                    <a name="/s:Sz8isSignedSbvpZ"></a>
                    <a name="//apple_ref/swift/Variable/isSigned" class="dashAnchor"></a>
                    <a class="token" href="#/s:Sz8isSignedSbvpZ">isSigned</a>
                    </code>
                  </div>
                  <div class="height-container">
                    <div class="pointer-container"></div>
                    <section class="section">
                      <div class="pointer"></div>
                      <div class="abstract">
                        
                      </div>
                      <div class="declaration">
                        <h4>Declaration</h4>
                        <div class="language">
                          <p class="aside-title">Swift</p>
                          <pre class="highlight swift"><code><span class="kd">public</span> <span class="kd">static</span> <span class="k">var</span> <span class="nv">isSigned</span><span class="p">:</span> <span class="kt">Bool</span> <span class="p">{</span> <span class="k">get</span> <span class="p">}</span></code></pre>

                        </div>
                      </div>
                      <div class="slightly-smaller">
                        <a href="https://github.com/attaswift/tree/v5.2.1/Sources/BigInt.swift#L40-L42">Show on GitHub</a>
                      </div>
                    </section>
                  </div>
                </li>
                <li class="item">
                  <div>
                    <code>
                    <a name="/s:6BigIntAAV9magnitudeAA0A4UIntVvp"></a>
                    <a name="//apple_ref/swift/Property/magnitude" class="dashAnchor"></a>
                    <a class="token" href="#/s:6BigIntAAV9magnitudeAA0A4UIntVvp">magnitude</a>
                    </code>
                  </div>
                  <div class="height-container">
                    <div class="pointer-container"></div>
                    <section class="section">
                      <div class="pointer"></div>
                      <div class="abstract">
                        <p>The absolute value of this integer.</p>

                      </div>
                      <div class="declaration">
                        <h4>Declaration</h4>
                        <div class="language">
                          <p class="aside-title">Swift</p>
                          <pre class="highlight swift"><code><span class="kd">public</span> <span class="k">var</span> <span class="nv">magnitude</span><span class="p">:</span> <span class="kt"><a href="../Structs/BigUInt.html">BigUInt</a></span></code></pre>

                        </div>
                      </div>
                      <div class="slightly-smaller">
                        <a href="https://github.com/attaswift/tree/v5.2.1/Sources/BigInt.swift#L45">Show on GitHub</a>
                      </div>
                    </section>
                  </div>
                </li>
                <li class="item">
                  <div>
                    <code>
                    <a name="/s:6BigIntAAV4signAB4SignOvp"></a>
                    <a name="//apple_ref/swift/Property/sign" class="dashAnchor"></a>
                    <a class="token" href="#/s:6BigIntAAV4signAB4SignOvp">sign</a>
                    </code>
                  </div>
                  <div class="height-container">
                    <div class="pointer-container"></div>
                    <section class="section">
                      <div class="pointer"></div>
                      <div class="abstract">
                        <p>True iff the value of this integer is negative.</p>

                      </div>
                      <div class="declaration">
                        <h4>Declaration</h4>
                        <div class="language">
                          <p class="aside-title">Swift</p>
                          <pre class="highlight swift"><code><span class="kd">public</span> <span class="k">var</span> <span class="nv">sign</span><span class="p">:</span> <span class="kt"><a href="../Structs/BigInt/Sign.html">Sign</a></span></code></pre>

                        </div>
                      </div>
                      <div class="slightly-smaller">
                        <a href="https://github.com/attaswift/tree/v5.2.1/Sources/BigInt.swift#L48">Show on GitHub</a>
                      </div>
                    </section>
                  </div>
                </li>
                <li class="item">
                  <div>
                    <code>
                    <a name="/s:6BigIntAAV4sign9magnitudeA2B4SignO_AA0A4UIntVtcfc"></a>
                    <a name="//apple_ref/swift/Method/init(sign:magnitude:)" class="dashAnchor"></a>
                    <a class="token" href="#/s:6BigIntAAV4sign9magnitudeA2B4SignO_AA0A4UIntVtcfc">init(sign:<wbr>magnitude:<wbr>)</a>
                    </code>
                  </div>
                  <div class="height-container">
                    <div class="pointer-container"></div>
                    <section class="section">
                      <div class="pointer"></div>
                      <div class="abstract">
                        <p>Initializes a new big integer with the provided absolute number and sign flag.</p>

                      </div>
                      <div class="declaration">
                        <h4>Declaration</h4>
                        <div class="language">
                          <p class="aside-title">Swift</p>
                          <pre class="highlight swift"><code><span class="kd">public</span> <span class="nf">init</span><span class="p">(</span><span class="nv">sign</span><span class="p">:</span> <span class="kt"><a href="../Structs/BigInt/Sign.html">Sign</a></span><span class="p">,</span> <span class="nv">magnitude</span><span class="p">:</span> <span class="kt"><a href="../Structs/BigUInt.html">BigUInt</a></span><span class="p">)</span></code></pre>

                        </div>
                      </div>
                      <div class="slightly-smaller">
                        <a href="https://github.com/attaswift/tree/v5.2.1/Sources/BigInt.swift#L51-L54">Show on GitHub</a>
                      </div>
                    </section>
                  </div>
                </li>
                <li class="item">
                  <div>
                    <code>
                    <a name="/s:6BigIntAAV6isZeroSbvp"></a>
                    <a name="//apple_ref/swift/Property/isZero" class="dashAnchor"></a>
                    <a class="token" href="#/s:6BigIntAAV6isZeroSbvp">isZero</a>
                    </code>
                  </div>
                  <div class="height-container">
                    <div class="pointer-container"></div>
                    <section class="section">
                      <div class="pointer"></div>
                      <div class="abstract">
                        <p>Return true iff this integer is zero.</p>
<div class="aside aside-complexity">
    <p class="aside-title">Complexity</p>
    O(1)

</div>

                      </div>
                      <div class="declaration">
                        <h4>Declaration</h4>
                        <div class="language">
                          <p class="aside-title">Swift</p>
                          <pre class="highlight swift"><code><span class="kd">public</span> <span class="k">var</span> <span class="nv">isZero</span><span class="p">:</span> <span class="kt">Bool</span> <span class="p">{</span> <span class="k">get</span> <span class="p">}</span></code></pre>

                        </div>
                      </div>
                      <div class="slightly-smaller">
                        <a href="https://github.com/attaswift/tree/v5.2.1/Sources/BigInt.swift#L59-L61">Show on GitHub</a>
                      </div>
                    </section>
                  </div>
                </li>
                <li class="item">
                  <div>
                    <code>
                    <a name="/s:6BigIntAAV6signumAByF"></a>
                    <a name="//apple_ref/swift/Method/signum()" class="dashAnchor"></a>
                    <a class="token" href="#/s:6BigIntAAV6signumAByF">signum()</a>
                    </code>
                  </div>
                  <div class="height-container">
                    <div class="pointer-container"></div>
                    <section class="section">
                      <div class="pointer"></div>
                      <div class="abstract">
                        <p>Returns <code>-1</code> if this value is negative and <code>1</code> if it’s positive; otherwise, <code>0</code>.</p>

                      </div>
                      <div class="declaration">
                        <h4>Declaration</h4>
                        <div class="language">
                          <p class="aside-title">Swift</p>
                          <pre class="highlight swift"><code><span class="kd">public</span> <span class="kd">func</span> <span class="nf">signum</span><span class="p">()</span> <span class="o">-&gt;</span> <span class="kt">BigInt</span></code></pre>

                        </div>
                      </div>
                      <div>
                        <h4>Return Value</h4>
                        <p>The sign of this number, expressed as an integer of the same type.</p>
                      </div>
                      <div class="slightly-smaller">
                        <a href="https://github.com/attaswift/tree/v5.2.1/Sources/BigInt.swift#L66-L73">Show on GitHub</a>
                      </div>
                    </section>
                  </div>
                </li>
                <li class="item">
                  <div>
                    <code>
                    <a name="/s:6BigIntAAV1poiyA2B_ABtFZ"></a>
                    <a name="//apple_ref/swift/Method/+(_:_:)" class="dashAnchor"></a>
                    <a class="token" href="#/s:6BigIntAAV1poiyA2B_ABtFZ">+(_:<wbr>_:<wbr>)</a>
                    </code>
                  </div>
                  <div class="height-container">
                    <div class="pointer-container"></div>
                    <section class="section">
                      <div class="pointer"></div>
                      <div class="abstract">
                        <p>Add <code>a</code> to <code>b</code> and return the result.</p>

                      </div>
                      <div class="declaration">
                        <h4>Declaration</h4>
                        <div class="language">
                          <p class="aside-title">Swift</p>
                          <pre class="highlight swift"><code><span class="kd">public</span> <span class="kd">static</span> <span class="kd">func</span> <span class="o">+</span> <span class="p">(</span><span class="nv">a</span><span class="p">:</span> <span class="kt">BigInt</span><span class="p">,</span> <span class="nv">b</span><span class="p">:</span> <span class="kt">BigInt</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="kt">BigInt</span></code></pre>

                        </div>
                      </div>
                      <div class="slightly-smaller">
                        <a href="https://github.com/attaswift/tree/v5.2.1/Sources/Addition.swift#L98-L119">Show on GitHub</a>
                      </div>
                    </section>
                  </div>
                </li>
                <li class="item">
                  <div>
                    <code>
                    <a name="/s:6BigIntAAV2peoiyyABz_ABtFZ"></a>
                    <a name="//apple_ref/swift/Method/+=(_:_:)" class="dashAnchor"></a>
                    <a class="token" href="#/s:6BigIntAAV2peoiyyABz_ABtFZ">+=(_:<wbr>_:<wbr>)</a>
                    </code>
                  </div>
                  <div class="height-container">
                    <div class="pointer-container"></div>
                    <section class="section">
                      <div class="pointer"></div>
                      <div class="abstract">
                        <p>Add <code>b</code> to <code>a</code> in place.</p>

                      </div>
                      <div class="declaration">
                        <h4>Declaration</h4>
                        <div class="language">
                          <p class="aside-title">Swift</p>
                          <pre class="highlight swift"><code><span class="kd">public</span> <span class="kd">static</span> <span class="kd">func</span> <span class="o">+=</span> <span class="p">(</span><span class="nv">a</span><span class="p">:</span> <span class="k">inout</span> <span class="kt">BigInt</span><span class="p">,</span> <span class="nv">b</span><span class="p">:</span> <span class="kt">BigInt</span><span class="p">)</span></code></pre>

                        </div>
                      </div>
                      <div class="slightly-smaller">
                        <a href="https://github.com/attaswift/tree/v5.2.1/Sources/Addition.swift#L122-L124">Show on GitHub</a>
                      </div>
                    </section>
                  </div>
                </li>
              </ul>
            </div>
            <div class="task-group">
              <div class="task-name-container">
                <a name="/Bitwise%20Operations"></a>
                <a name="//apple_ref/swift/Section/Bitwise Operations" class="dashAnchor"></a>
                <div class="section-name-container">
                  <a class="section-name-link" href="#/Bitwise%20Operations"></a>
                  <h3 class="section-name"><p>Bitwise Operations</p>
</h3>
                </div>
              </div>
              <ul class="item-container">
                <li class="item">
                  <div>
                    <code>
                    <a name="/s:6BigIntAAV1topyA2BFZ"></a>
                    <a name="//apple_ref/swift/Method/~(_:)" class="dashAnchor"></a>
                    <a class="token" href="#/s:6BigIntAAV1topyA2BFZ">~(_:<wbr>)</a>
                    </code>
                  </div>
                  <div class="height-container">
                    <div class="pointer-container"></div>
                    <section class="section">
                      <div class="pointer"></div>
                      <div class="abstract">
                        <p>Undocumented</p>

                      </div>
                      <div class="declaration">
                        <h4>Declaration</h4>
                        <div class="language">
                          <p class="aside-title">Swift</p>
                          <pre class="highlight swift"><code><span class="kd">public</span> <span class="k">prefix</span> <span class="kd">static</span> <span class="kd">func</span> <span class="o">~</span> <span class="p">(</span><span class="nv">x</span><span class="p">:</span> <span class="kt">BigInt</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="kt">BigInt</span></code></pre>

                        </div>
                      </div>
                      <div class="slightly-smaller">
                        <a href="https://github.com/attaswift/tree/v5.2.1/Sources/Bitwise Ops.swift#L50-L57">Show on GitHub</a>
                      </div>
                    </section>
                  </div>
                </li>
                <li class="item">
                  <div>
                    <code>
                    <a name="/s:6BigIntAAV1aoiyA2Bz_ABtFZ"></a>
                    <a name="//apple_ref/swift/Method/&amp;(_:_:)" class="dashAnchor"></a>
                    <a class="token" href="#/s:6BigIntAAV1aoiyA2Bz_ABtFZ">&(_:<wbr>_:<wbr>)</a>
                    </code>
                  </div>
                  <div class="height-container">
                    <div class="pointer-container"></div>
                    <section class="section">
                      <div class="pointer"></div>
                      <div class="abstract">
                        <p>Undocumented</p>

                      </div>
                      <div class="declaration">
                        <h4>Declaration</h4>
                        <div class="language">
                          <p class="aside-title">Swift</p>
                          <pre class="highlight swift"><code><span class="kd">public</span> <span class="kd">static</span> <span class="kd">func</span> <span class="o">&amp;</span> <span class="p">(</span><span class="nv">lhs</span><span class="p">:</span> <span class="k">inout</span> <span class="kt">BigInt</span><span class="p">,</span> <span class="nv">rhs</span><span class="p">:</span> <span class="kt">BigInt</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="kt">BigInt</span></code></pre>

                        </div>
                      </div>
                      <div class="slightly-smaller">
                        <a href="https://github.com/attaswift/tree/v5.2.1/Sources/Bitwise Ops.swift#L59-L74">Show on GitHub</a>
                      </div>
                    </section>
                  </div>
                </li>
                <li class="item">
                  <div>
                    <code>
                    <a name="/s:6BigIntAAV1ooiyA2Bz_ABtFZ"></a>
                    <a name="//apple_ref/swift/Method/|(_:_:)" class="dashAnchor"></a>
                    <a class="token" href="#/s:6BigIntAAV1ooiyA2Bz_ABtFZ">|(_:<wbr>_:<wbr>)</a>
                    </code>
                  </div>
                  <div class="height-container">
                    <div class="pointer-container"></div>
                    <section class="section">
                      <div class="pointer"></div>
                      <div class="abstract">
                        <p>Undocumented</p>

                      </div>
                      <div class="declaration">
                        <h4>Declaration</h4>
                        <div class="language">
                          <p class="aside-title">Swift</p>
                          <pre class="highlight swift"><code><span class="kd">public</span> <span class="kd">static</span> <span class="kd">func</span> <span class="o">|</span> <span class="p">(</span><span class="nv">lhs</span><span class="p">:</span> <span class="k">inout</span> <span class="kt">BigInt</span><span class="p">,</span> <span class="nv">rhs</span><span class="p">:</span> <span class="kt">BigInt</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="kt">BigInt</span></code></pre>

                        </div>
                      </div>
                      <div class="slightly-smaller">
                        <a href="https://github.com/attaswift/tree/v5.2.1/Sources/Bitwise Ops.swift#L76-L91">Show on GitHub</a>
                      </div>
                    </section>
                  </div>
                </li>
                <li class="item">
                  <div>
                    <code>
                    <a name="/s:6BigIntAAV1xoiyA2Bz_ABtFZ"></a>
                    <a name="//apple_ref/swift/Method/^(_:_:)" class="dashAnchor"></a>
                    <a class="token" href="#/s:6BigIntAAV1xoiyA2Bz_ABtFZ">^(_:<wbr>_:<wbr>)</a>
                    </code>
                  </div>
                  <div class="height-container">
                    <div class="pointer-container"></div>
                    <section class="section">
                      <div class="pointer"></div>
                      <div class="abstract">
                        <p>Undocumented</p>

                      </div>
                      <div class="declaration">
                        <h4>Declaration</h4>
                        <div class="language">
                          <p class="aside-title">Swift</p>
                          <pre class="highlight swift"><code><span class="kd">public</span> <span class="kd">static</span> <span class="kd">func</span> <span class="o">^</span> <span class="p">(</span><span class="nv">lhs</span><span class="p">:</span> <span class="k">inout</span> <span class="kt">BigInt</span><span class="p">,</span> <span class="nv">rhs</span><span class="p">:</span> <span class="kt">BigInt</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="kt">BigInt</span></code></pre>

                        </div>
                      </div>
                      <div class="slightly-smaller">
                        <a href="https://github.com/attaswift/tree/v5.2.1/Sources/Bitwise Ops.swift#L93-L108">Show on GitHub</a>
                      </div>
                    </section>
                  </div>
                </li>
                <li class="item">
                  <div>
                    <code>
                    <a name="/s:6BigIntAAV2aeoiyyABz_ABtFZ"></a>
                    <a name="//apple_ref/swift/Method/&amp;=(_:_:)" class="dashAnchor"></a>
                    <a class="token" href="#/s:6BigIntAAV2aeoiyyABz_ABtFZ">&=(_:<wbr>_:<wbr>)</a>
                    </code>
                  </div>
                  <div class="height-container">
                    <div class="pointer-container"></div>
                    <section class="section">
                      <div class="pointer"></div>
                      <div class="abstract">
                        <p>Undocumented</p>

                      </div>
                      <div class="declaration">
                        <h4>Declaration</h4>
                        <div class="language">
                          <p class="aside-title">Swift</p>
                          <pre class="highlight swift"><code><span class="kd">public</span> <span class="kd">static</span> <span class="kd">func</span> <span class="o">&amp;=</span> <span class="p">(</span><span class="nv">lhs</span><span class="p">:</span> <span class="k">inout</span> <span class="kt">BigInt</span><span class="p">,</span> <span class="nv">rhs</span><span class="p">:</span> <span class="kt">BigInt</span><span class="p">)</span></code></pre>

                        </div>
                      </div>
                      <div class="slightly-smaller">
                        <a href="https://github.com/attaswift/tree/v5.2.1/Sources/Bitwise Ops.swift#L110-L112">Show on GitHub</a>
                      </div>
                    </section>
                  </div>
                </li>
                <li class="item">
                  <div>
                    <code>
                    <a name="/s:6BigIntAAV2oeoiyyABz_ABtFZ"></a>
                    <a name="//apple_ref/swift/Method/|=(_:_:)" class="dashAnchor"></a>
                    <a class="token" href="#/s:6BigIntAAV2oeoiyyABz_ABtFZ">|=(_:<wbr>_:<wbr>)</a>
                    </code>
                  </div>
                  <div class="height-container">
                    <div class="pointer-container"></div>
                    <section class="section">
                      <div class="pointer"></div>
                      <div class="abstract">
                        <p>Undocumented</p>

                      </div>
                      <div class="declaration">
                        <h4>Declaration</h4>
                        <div class="language">
                          <p class="aside-title">Swift</p>
                          <pre class="highlight swift"><code><span class="kd">public</span> <span class="kd">static</span> <span class="kd">func</span> <span class="o">|=</span> <span class="p">(</span><span class="nv">lhs</span><span class="p">:</span> <span class="k">inout</span> <span class="kt">BigInt</span><span class="p">,</span> <span class="nv">rhs</span><span class="p">:</span> <span class="kt">BigInt</span><span class="p">)</span></code></pre>

                        </div>
                      </div>
                      <div class="slightly-smaller">
                        <a href="https://github.com/attaswift/tree/v5.2.1/Sources/Bitwise Ops.swift#L114-L116">Show on GitHub</a>
                      </div>
                    </section>
                  </div>
                </li>
                <li class="item">
                  <div>
                    <code>
                    <a name="/s:6BigIntAAV2xeoiyyABz_ABtFZ"></a>
                    <a name="//apple_ref/swift/Method/^=(_:_:)" class="dashAnchor"></a>
                    <a class="token" href="#/s:6BigIntAAV2xeoiyyABz_ABtFZ">^=(_:<wbr>_:<wbr>)</a>
                    </code>
                  </div>
                  <div class="height-container">
                    <div class="pointer-container"></div>
                    <section class="section">
                      <div class="pointer"></div>
                      <div class="abstract">
                        <p>Undocumented</p>

                      </div>
                      <div class="declaration">
                        <h4>Declaration</h4>
                        <div class="language">
                          <p class="aside-title">Swift</p>
                          <pre class="highlight swift"><code><span class="kd">public</span> <span class="kd">static</span> <span class="kd">func</span> <span class="o">^=</span> <span class="p">(</span><span class="nv">lhs</span><span class="p">:</span> <span class="k">inout</span> <span class="kt">BigInt</span><span class="p">,</span> <span class="nv">rhs</span><span class="p">:</span> <span class="kt">BigInt</span><span class="p">)</span></code></pre>

                        </div>
                      </div>
                      <div class="slightly-smaller">
                        <a href="https://github.com/attaswift/tree/v5.2.1/Sources/Bitwise Ops.swift#L118-L120">Show on GitHub</a>
                      </div>
                    </section>
                  </div>
                </li>
                <li class="item">
                  <div>
                    <code>
                    <a name="/s:Se4fromxs7Decoder_p_tKcfc"></a>
                    <a name="//apple_ref/swift/Method/init(from:)" class="dashAnchor"></a>
                    <a class="token" href="#/s:Se4fromxs7Decoder_p_tKcfc">init(from:<wbr>)</a>
                    </code>
                  </div>
                  <div class="height-container">
                    <div class="pointer-container"></div>
                    <section class="section">
                      <div class="pointer"></div>
                      <div class="abstract">
                        
                      </div>
                      <div class="declaration">
                        <h4>Declaration</h4>
                        <div class="language">
                          <p class="aside-title">Swift</p>
                          <pre class="highlight swift"><code><span class="kd">public</span> <span class="nf">init</span><span class="p">(</span><span class="n">from</span> <span class="nv">decoder</span><span class="p">:</span> <span class="kt">Decoder</span><span class="p">)</span> <span class="k">throws</span></code></pre>

                        </div>
                      </div>
                      <div class="slightly-smaller">
                        <a href="https://github.com/attaswift/tree/v5.2.1/Sources/Codable.swift#L104-L127">Show on GitHub</a>
                      </div>
                    </section>
                  </div>
                </li>
                <li class="item">
                  <div>
                    <code>
                    <a name="/s:SE6encode2toys7Encoder_p_tKF"></a>
                    <a name="//apple_ref/swift/Method/encode(to:)" class="dashAnchor"></a>
                    <a class="token" href="#/s:SE6encode2toys7Encoder_p_tKF">encode(to:<wbr>)</a>
                    </code>
                  </div>
                  <div class="height-container">
                    <div class="pointer-container"></div>
                    <section class="section">
                      <div class="pointer"></div>
                      <div class="abstract">
                        
                      </div>
                      <div class="declaration">
                        <h4>Declaration</h4>
                        <div class="language">
                          <p class="aside-title">Swift</p>
                          <pre class="highlight swift"><code><span class="kd">public</span> <span class="kd">func</span> <span class="nf">encode</span><span class="p">(</span><span class="n">to</span> <span class="nv">encoder</span><span class="p">:</span> <span class="kt">Encoder</span><span class="p">)</span> <span class="k">throws</span></code></pre>

                        </div>
                      </div>
                      <div class="slightly-smaller">
                        <a href="https://github.com/attaswift/tree/v5.2.1/Sources/Codable.swift#L129-L139">Show on GitHub</a>
                      </div>
                    </section>
                  </div>
                </li>
                <li class="item">
                  <div>
                    <code>
                    <a name="/s:6BigIntAAV2eeoiySbAB_ABtFZ"></a>
                    <a name="//apple_ref/swift/Method/==(_:_:)" class="dashAnchor"></a>
                    <a class="token" href="#/s:6BigIntAAV2eeoiySbAB_ABtFZ">==(_:<wbr>_:<wbr>)</a>
                    </code>
                  </div>
                  <div class="height-container">
                    <div class="pointer-container"></div>
                    <section class="section">
                      <div class="pointer"></div>
                      <div class="abstract">
                        <p>Return true iff <code>a</code> is equal to <code>b</code>.</p>

                      </div>
                      <div class="declaration">
                        <h4>Declaration</h4>
                        <div class="language">
                          <p class="aside-title">Swift</p>
                          <pre class="highlight swift"><code><span class="kd">public</span> <span class="kd">static</span> <span class="kd">func</span> <span class="o">==</span> <span class="p">(</span><span class="nv">a</span><span class="p">:</span> <span class="kt">BigInt</span><span class="p">,</span> <span class="nv">b</span><span class="p">:</span> <span class="kt">BigInt</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="kt">Bool</span></code></pre>

                        </div>
                      </div>
                      <div class="slightly-smaller">
                        <a href="https://github.com/attaswift/tree/v5.2.1/Sources/Comparable.swift#L44-L46">Show on GitHub</a>
                      </div>
                    </section>
                  </div>
                </li>
                <li class="item">
                  <div>
                    <code>
                    <a name="/s:6BigIntAAV1loiySbAB_ABtFZ"></a>
                    <a name="//apple_ref/swift/Method/&lt;(_:_:)" class="dashAnchor"></a>
                    <a class="token" href="#/s:6BigIntAAV1loiySbAB_ABtFZ"><(_:<wbr>_:<wbr>)</a>
                    </code>
                  </div>
                  <div class="height-container">
                    <div class="pointer-container"></div>
                    <section class="section">
                      <div class="pointer"></div>
                      <div class="abstract">
                        <p>Return true iff <code>a</code> is less than <code>b</code>.</p>

                      </div>
                      <div class="declaration">
                        <h4>Declaration</h4>
                        <div class="language">
                          <p class="aside-title">Swift</p>
                          <pre class="highlight swift"><code><span class="kd">public</span> <span class="kd">static</span> <span class="kd">func</span> <span class="o">&lt;</span> <span class="p">(</span><span class="nv">a</span><span class="p">:</span> <span class="kt">BigInt</span><span class="p">,</span> <span class="nv">b</span><span class="p">:</span> <span class="kt">BigInt</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="kt">Bool</span></code></pre>

                        </div>
                      </div>
                      <div class="slightly-smaller">
                        <a href="https://github.com/attaswift/tree/v5.2.1/Sources/Comparable.swift#L49-L60">Show on GitHub</a>
                      </div>
                    </section>
                  </div>
                </li>
                <li class="item">
                  <div>
                    <code>
                    <a name="/s:6BigIntAAVyABSWcfc"></a>
                    <a name="//apple_ref/swift/Method/init(_:)" class="dashAnchor"></a>
                    <a class="token" href="#/s:6BigIntAAVyABSWcfc">init(_:<wbr>)</a>
                    </code>
                  </div>
                  <div class="height-container">
                    <div class="pointer-container"></div>
                    <section class="section">
                      <div class="pointer"></div>
                      <div class="abstract">
                        <p>Initialize a BigInt from bytes accessed from an UnsafeRawBufferPointer,
where the first byte indicates sign (0 for positive, 1 for negative)</p>

                      </div>
                      <div class="declaration">
                        <h4>Declaration</h4>
                        <div class="language">
                          <p class="aside-title">Swift</p>
                          <pre class="highlight swift"><code><span class="kd">public</span> <span class="nf">init</span><span class="p">(</span><span class="n">_</span> <span class="nv">buffer</span><span class="p">:</span> <span class="kt">UnsafeRawBufferPointer</span><span class="p">)</span></code></pre>

                        </div>
                      </div>
                      <div class="slightly-smaller">
                        <a href="https://github.com/attaswift/tree/v5.2.1/Sources/Data Conversion.swift#L116-L135">Show on GitHub</a>
                      </div>
                    </section>
                  </div>
                </li>
                <li class="item">
                  <div>
                    <code>
                    <a name="/s:6BigIntAAVyAB10Foundation4DataVcfc"></a>
                    <a name="//apple_ref/swift/Method/init(_:)" class="dashAnchor"></a>
                    <a class="token" href="#/s:6BigIntAAVyAB10Foundation4DataVcfc">init(_:<wbr>)</a>
                    </code>
                  </div>
                  <div class="height-container">
                    <div class="pointer-container"></div>
                    <section class="section">
                      <div class="pointer"></div>
                      <div class="abstract">
                        <p>Initializes an integer from the bits stored inside a piece of <code>Data</code>.
The data is assumed to be in network (big-endian) byte order with a first
byte to represent the sign (0 for positive, 1 for negative)</p>

                      </div>
                      <div class="declaration">
                        <h4>Declaration</h4>
                        <div class="language">
                          <p class="aside-title">Swift</p>
                          <pre class="highlight swift"><code><span class="kd">public</span> <span class="nf">init</span><span class="p">(</span><span class="n">_</span> <span class="nv">data</span><span class="p">:</span> <span class="kt">Data</span><span class="p">)</span></code></pre>

                        </div>
                      </div>
                      <div class="slightly-smaller">
                        <a href="https://github.com/attaswift/tree/v5.2.1/Sources/Data Conversion.swift#L140-L159">Show on GitHub</a>
                      </div>
                    </section>
                  </div>
                </li>
                <li class="item">
                  <div>
                    <code>
                    <a name="/s:6BigIntAAV9serialize10Foundation4DataVyF"></a>
                    <a name="//apple_ref/swift/Method/serialize()" class="dashAnchor"></a>
                    <a class="token" href="#/s:6BigIntAAV9serialize10Foundation4DataVyF">serialize()</a>
                    </code>
                  </div>
                  <div class="height-container">
                    <div class="pointer-container"></div>
                    <section class="section">
                      <div class="pointer"></div>
                      <div class="abstract">
                        <p>Return a <code>Data</code> value that contains the base-256 representation of this integer, in network (big-endian) byte order and a prepended byte to indicate the sign (0 for positive, 1 for negative)</p>

                      </div>
                      <div class="declaration">
                        <h4>Declaration</h4>
                        <div class="language">
                          <p class="aside-title">Swift</p>
                          <pre class="highlight swift"><code><span class="kd">public</span> <span class="kd">func</span> <span class="nf">serialize</span><span class="p">()</span> <span class="o">-&gt;</span> <span class="kt">Data</span></code></pre>

                        </div>
                      </div>
                      <div class="slightly-smaller">
                        <a href="https://github.com/attaswift/tree/v5.2.1/Sources/Data Conversion.swift#L162-L178">Show on GitHub</a>
                      </div>
                    </section>
                  </div>
                </li>
              </ul>
            </div>
            <div class="task-group">
              <div class="task-name-container">
                <a name="/Full-width%20multiplication%20and%20division"></a>
                <a name="//apple_ref/swift/Section/Full-width multiplication and division" class="dashAnchor"></a>
                <div class="section-name-container">
                  <a class="section-name-link" href="#/Full-width%20multiplication%20and%20division"></a>
                  <h3 class="section-name"><p>Full-width multiplication and division</p>
</h3>
                </div>
              </div>
              <ul class="item-container">
                <li class="item">
                  <div>
                    <code>
                    <a name="/s:6BigIntAAV20quotientAndRemainder10dividingByAB0C0_AB9remaindertAB_tF"></a>
                    <a name="//apple_ref/swift/Method/quotientAndRemainder(dividingBy:)" class="dashAnchor"></a>
                    <a class="token" href="#/s:6BigIntAAV20quotientAndRemainder10dividingByAB0C0_AB9remaindertAB_tF">quotientAndRemainder(dividingBy:<wbr>)</a>
                    </code>
                  </div>
                  <div class="height-container">
                    <div class="pointer-container"></div>
                    <section class="section">
                      <div class="pointer"></div>
                      <div class="abstract">
                        <p>Divide this integer by <code>y</code> and return the resulting quotient and remainder.</p>
<div class="aside aside-requires">
    <p class="aside-title">Requires</p>
    <code>y &gt; 0</code>

</div><div class="aside aside-complexity">
    <p class="aside-title">Complexity</p>
    O(count^2)

</div>

                      </div>
                      <div class="declaration">
                        <h4>Declaration</h4>
                        <div class="language">
                          <p class="aside-title">Swift</p>
                          <pre class="highlight swift"><code><span class="kd">public</span> <span class="kd">func</span> <span class="nf">quotientAndRemainder</span><span class="p">(</span><span class="n">dividingBy</span> <span class="nv">y</span><span class="p">:</span> <span class="kt">BigInt</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="p">(</span><span class="nv">quotient</span><span class="p">:</span> <span class="kt">BigInt</span><span class="p">,</span> <span class="nv">remainder</span><span class="p">:</span> <span class="kt">BigInt</span><span class="p">)</span></code></pre>

                        </div>
                      </div>
                      <div>
                        <h4>Return Value</h4>
                        <p><code>(quotient, remainder)</code> where <code>quotient = floor(self/y)</code>, <code>remainder = self - quotient * y</code></p>
                      </div>
                      <div class="slightly-smaller">
                        <a href="https://github.com/attaswift/tree/v5.2.1/Sources/Division.swift#L342-L348">Show on GitHub</a>
                      </div>
                    </section>
                  </div>
                </li>
                <li class="item">
                  <div>
                    <code>
                    <a name="/s:6BigIntAAV1doiyA2B_ABtFZ"></a>
                    <a name="//apple_ref/swift/Method//(_:_:)" class="dashAnchor"></a>
                    <a class="token" href="#/s:6BigIntAAV1doiyA2B_ABtFZ">/(_:<wbr>_:<wbr>)</a>
                    </code>
                  </div>
                  <div class="height-container">
                    <div class="pointer-container"></div>
                    <section class="section">
                      <div class="pointer"></div>
                      <div class="abstract">
                        <p>Divide <code>a</code> by <code>b</code> and return the quotient. Traps if <code>b</code> is zero.</p>

                      </div>
                      <div class="declaration">
                        <h4>Declaration</h4>
                        <div class="language">
                          <p class="aside-title">Swift</p>
                          <pre class="highlight swift"><code><span class="kd">public</span> <span class="kd">static</span> <span class="kd">func</span> <span class="o">/</span> <span class="p">(</span><span class="nv">a</span><span class="p">:</span> <span class="kt">BigInt</span><span class="p">,</span> <span class="nv">b</span><span class="p">:</span> <span class="kt">BigInt</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="kt">BigInt</span></code></pre>

                        </div>
                      </div>
                      <div class="slightly-smaller">
                        <a href="https://github.com/attaswift/tree/v5.2.1/Sources/Division.swift#L351-L353">Show on GitHub</a>
                      </div>
                    </section>
                  </div>
                </li>
                <li class="item">
                  <div>
                    <code>
                    <a name="/s:6BigIntAAV1roiyA2B_ABtFZ"></a>
                    <a name="//apple_ref/swift/Method/%(_:_:)" class="dashAnchor"></a>
                    <a class="token" href="#/s:6BigIntAAV1roiyA2B_ABtFZ">%(_:<wbr>_:<wbr>)</a>
                    </code>
                  </div>
                  <div class="height-container">
                    <div class="pointer-container"></div>
                    <section class="section">
                      <div class="pointer"></div>
                      <div class="abstract">
                        <p>Divide <code>a</code> by <code>b</code> and return the remainder. The result has the same sign as <code>a</code>.</p>

                      </div>
                      <div class="declaration">
                        <h4>Declaration</h4>
                        <div class="language">
                          <p class="aside-title">Swift</p>
                          <pre class="highlight swift"><code><span class="kd">public</span> <span class="kd">static</span> <span class="kd">func</span> <span class="o">%</span> <span class="p">(</span><span class="nv">a</span><span class="p">:</span> <span class="kt">BigInt</span><span class="p">,</span> <span class="nv">b</span><span class="p">:</span> <span class="kt">BigInt</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="kt">BigInt</span></code></pre>

                        </div>
                      </div>
                      <div class="slightly-smaller">
                        <a href="https://github.com/attaswift/tree/v5.2.1/Sources/Division.swift#L356-L358">Show on GitHub</a>
                      </div>
                    </section>
                  </div>
                </li>
                <li class="item">
                  <div>
                    <code>
                    <a name="/s:6BigIntAAV7modulusyA2BF"></a>
                    <a name="//apple_ref/swift/Method/modulus(_:)" class="dashAnchor"></a>
                    <a class="token" href="#/s:6BigIntAAV7modulusyA2BF">modulus(_:<wbr>)</a>
                    </code>
                  </div>
                  <div class="height-container">
                    <div class="pointer-container"></div>
                    <section class="section">
                      <div class="pointer"></div>
                      <div class="abstract">
                        <p>Return the result of <code>a</code> mod <code>b</code>. The result is always a nonnegative integer that is less than the absolute value of <code>b</code>.</p>

                      </div>
                      <div class="declaration">
                        <h4>Declaration</h4>
                        <div class="language">
                          <p class="aside-title">Swift</p>
                          <pre class="highlight swift"><code><span class="kd">public</span> <span class="kd">func</span> <span class="nf">modulus</span><span class="p">(</span><span class="n">_</span> <span class="nv">mod</span><span class="p">:</span> <span class="kt">BigInt</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="kt">BigInt</span></code></pre>

                        </div>
                      </div>
                      <div class="slightly-smaller">
                        <a href="https://github.com/attaswift/tree/v5.2.1/Sources/Division.swift#L361-L367">Show on GitHub</a>
                      </div>
                    </section>
                  </div>
                </li>
                <li class="item">
                  <div>
                    <code>
                    <a name="/s:6BigIntAAV2deoiyyABz_ABtFZ"></a>
                    <a name="//apple_ref/swift/Method//=(_:_:)" class="dashAnchor"></a>
                    <a class="token" href="#/s:6BigIntAAV2deoiyyABz_ABtFZ">/=(_:<wbr>_:<wbr>)</a>
                    </code>
                  </div>
                  <div class="height-container">
                    <div class="pointer-container"></div>
                    <section class="section">
                      <div class="pointer"></div>
                      <div class="abstract">
                        <p>Divide <code>a</code> by <code>b</code> storing the quotient in <code>a</code>.</p>

                      </div>
                      <div class="declaration">
                        <h4>Declaration</h4>
                        <div class="language">
                          <p class="aside-title">Swift</p>
                          <pre class="highlight swift"><code><span class="kd">public</span> <span class="kd">static</span> <span class="kd">func</span> <span class="o">/=</span> <span class="p">(</span><span class="nv">a</span><span class="p">:</span> <span class="k">inout</span> <span class="kt">BigInt</span><span class="p">,</span> <span class="nv">b</span><span class="p">:</span> <span class="kt">BigInt</span><span class="p">)</span></code></pre>

                        </div>
                      </div>
                      <div class="slightly-smaller">
                        <a href="https://github.com/attaswift/tree/v5.2.1/Sources/Division.swift#L372">Show on GitHub</a>
                      </div>
                    </section>
                  </div>
                </li>
                <li class="item">
                  <div>
                    <code>
                    <a name="/s:6BigIntAAV2reoiyyABz_ABtFZ"></a>
                    <a name="//apple_ref/swift/Method/%=(_:_:)" class="dashAnchor"></a>
                    <a class="token" href="#/s:6BigIntAAV2reoiyyABz_ABtFZ">%=(_:<wbr>_:<wbr>)</a>
                    </code>
                  </div>
                  <div class="height-container">
                    <div class="pointer-container"></div>
                    <section class="section">
                      <div class="pointer"></div>
                      <div class="abstract">
                        <p>Divide <code>a</code> by <code>b</code> storing the remainder in <code>a</code>.</p>

                      </div>
                      <div class="declaration">
                        <h4>Declaration</h4>
                        <div class="language">
                          <p class="aside-title">Swift</p>
                          <pre class="highlight swift"><code><span class="kd">public</span> <span class="kd">static</span> <span class="kd">func</span> <span class="o">%=</span> <span class="p">(</span><span class="nv">a</span><span class="p">:</span> <span class="k">inout</span> <span class="kt">BigInt</span><span class="p">,</span> <span class="nv">b</span><span class="p">:</span> <span class="kt">BigInt</span><span class="p">)</span></code></pre>

                        </div>
                      </div>
                      <div class="slightly-smaller">
                        <a href="https://github.com/attaswift/tree/v5.2.1/Sources/Division.swift#L374">Show on GitHub</a>
                      </div>
                    </section>
                  </div>
                </li>
                <li class="item">
                  <div>
                    <code>
                    <a name="/s:6BigIntAAV5poweryABSiF"></a>
                    <a name="//apple_ref/swift/Method/power(_:)" class="dashAnchor"></a>
                    <a class="token" href="#/s:6BigIntAAV5poweryABSiF">power(_:<wbr>)</a>
                    </code>
                  </div>
                  <div class="height-container">
                    <div class="pointer-container"></div>
                    <section class="section">
                      <div class="pointer"></div>
                      <div class="abstract">
                        <p>Returns this integer raised to the power <code>exponent</code>.</p>

<p>This function calculates the result by <a href="https://en.wikipedia.org/wiki/Exponentiation_by_squaring">successively squaring the base while halving the exponent</a>.</p>
<div class="aside aside-note">
    <p class="aside-title">Note</p>
    This function can be unreasonably expensive for large exponents, which is why <code>exponent</code> is
    a simple integer value. If you want to calculate big exponents, you&rsquo;ll probably need to use
    the modulo arithmetic variant.

</div><div class="aside aside-see-also">
    <p class="aside-title">See also</p>
    <code>BigUInt.power(_:, modulus:)</code>

</div><div class="aside aside-complexity">
    <p class="aside-title">Complexity</p>
    O((exponent * self.count)^log2(3)) or somesuch. The result may require a large amount of memory, too.

</div>

                      </div>
                      <div class="declaration">
                        <h4>Declaration</h4>
                        <div class="language">
                          <p class="aside-title">Swift</p>
                          <pre class="highlight swift"><code><span class="kd">public</span> <span class="kd">func</span> <span class="nf">power</span><span class="p">(</span><span class="n">_</span> <span class="nv">exponent</span><span class="p">:</span> <span class="kt">Int</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="kt">BigInt</span></code></pre>

                        </div>
                      </div>
                      <div>
                        <h4>Return Value</h4>
                        <p>1 if <code>exponent == 0</code>, otherwise <code>self</code> raised to <code>exponent</code>. (This implies that <code>0.power(0) == 1</code>.)</p>
                      </div>
                      <div class="slightly-smaller">
                        <a href="https://github.com/attaswift/tree/v5.2.1/Sources/Exponentiation.swift#L88-L91">Show on GitHub</a>
                      </div>
                    </section>
                  </div>
                </li>
                <li class="item">
                  <div>
                    <code>
                    <a name="/s:6BigIntAAV5power_7modulusA2B_ABtF"></a>
                    <a name="//apple_ref/swift/Method/power(_:modulus:)" class="dashAnchor"></a>
                    <a class="token" href="#/s:6BigIntAAV5power_7modulusA2B_ABtF">power(_:<wbr>modulus:<wbr>)</a>
                    </code>
                  </div>
                  <div class="height-container">
                    <div class="pointer-container"></div>
                    <section class="section">
                      <div class="pointer"></div>
                      <div class="abstract">
                        <p>Returns the remainder of this integer raised to the power <code>exponent</code> in modulo arithmetic under <code>modulus</code>.</p>

<p>Uses the <a href="https://en.wikipedia.org/wiki/Modular_exponentiation#Right-to-left_binary_method">right-to-left binary method</a>.</p>
<div class="aside aside-complexity">
    <p class="aside-title">Complexity</p>
    O(exponent.count * modulus.count^log2(3)) or somesuch

</div>

                      </div>
                      <div class="declaration">
                        <h4>Declaration</h4>
                        <div class="language">
                          <p class="aside-title">Swift</p>
                          <pre class="highlight swift"><code><span class="kd">public</span> <span class="kd">func</span> <span class="nf">power</span><span class="p">(</span><span class="n">_</span> <span class="nv">exponent</span><span class="p">:</span> <span class="kt">BigInt</span><span class="p">,</span> <span class="nv">modulus</span><span class="p">:</span> <span class="kt">BigInt</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="kt">BigInt</span></code></pre>

                        </div>
                      </div>
                      <div class="slightly-smaller">
                        <a href="https://github.com/attaswift/tree/v5.2.1/Sources/Exponentiation.swift#L100-L118">Show on GitHub</a>
                      </div>
                    </section>
                  </div>
                </li>
                <li class="item">
                  <div>
                    <code>
                    <a name="/s:Sz7exactlyxSgqd___tcSBRd__lufc"></a>
                    <a name="//apple_ref/swift/Method/init(exactly:)" class="dashAnchor"></a>
                    <a class="token" href="#/s:Sz7exactlyxSgqd___tcSBRd__lufc">init(exactly:<wbr>)</a>
                    </code>
                  </div>
                  <div class="height-container">
                    <div class="pointer-container"></div>
                    <section class="section">
                      <div class="pointer"></div>
                      <div class="abstract">
                        
                      </div>
                      <div class="declaration">
                        <h4>Declaration</h4>
                        <div class="language">
                          <p class="aside-title">Swift</p>
                          <pre class="highlight swift"><code><span class="kd">public</span> <span class="kd">init</span><span class="p">?</span><span class="o">&lt;</span><span class="kt">T</span><span class="o">&gt;</span><span class="p">(</span><span class="n">exactly</span> <span class="nv">source</span><span class="p">:</span> <span class="kt">T</span><span class="p">)</span> <span class="k">where</span> <span class="kt">T</span> <span class="p">:</span> <span class="kt">BinaryFloatingPoint</span></code></pre>

                        </div>
                      </div>
                      <div class="slightly-smaller">
                        <a href="https://github.com/attaswift/tree/v5.2.1/Sources/Floating Point Conversion.swift#L28-L37">Show on GitHub</a>
                      </div>
                    </section>
                  </div>
                </li>
                <li class="item">
                  <div>
                    <code>
                    <a name="/s:Szyxqd__cSBRd__lufc"></a>
                    <a name="//apple_ref/swift/Method/init(_:)" class="dashAnchor"></a>
                    <a class="token" href="#/s:Szyxqd__cSBRd__lufc">init(_:<wbr>)</a>
                    </code>
                  </div>
                  <div class="height-container">
                    <div class="pointer-container"></div>
                    <section class="section">
                      <div class="pointer"></div>
                      <div class="abstract">
                        
                      </div>
                      <div class="declaration">
                        <h4>Declaration</h4>
                        <div class="language">
                          <p class="aside-title">Swift</p>
                          <pre class="highlight swift"><code><span class="kd">public</span> <span class="kd">init</span><span class="o">&lt;</span><span class="kt">T</span><span class="o">&gt;</span><span class="p">(</span><span class="n">_</span> <span class="nv">source</span><span class="p">:</span> <span class="kt">T</span><span class="p">)</span> <span class="k">where</span> <span class="kt">T</span> <span class="p">:</span> <span class="kt">BinaryFloatingPoint</span></code></pre>

                        </div>
                      </div>
                      <div class="slightly-smaller">
                        <a href="https://github.com/attaswift/tree/v5.2.1/Sources/Floating Point Conversion.swift#L39-L41">Show on GitHub</a>
                      </div>
                    </section>
                  </div>
                </li>
                <li class="item">
                  <div>
                    <code>
                    <a name="/s:6BigIntAAV21greatestCommonDivisor4withA2B_tF"></a>
                    <a name="//apple_ref/swift/Method/greatestCommonDivisor(with:)" class="dashAnchor"></a>
                    <a class="token" href="#/s:6BigIntAAV21greatestCommonDivisor4withA2B_tF">greatestCommonDivisor(with:<wbr>)</a>
                    </code>
                  </div>
                  <div class="height-container">
                    <div class="pointer-container"></div>
                    <section class="section">
                      <div class="pointer"></div>
                      <div class="abstract">
                        <p>Returns the greatest common divisor of <code>a</code> and <code>b</code>.</p>
<div class="aside aside-complexity">
    <p class="aside-title">Complexity</p>
    O(count^2) where count = max(a.count, b.count)

</div>

                      </div>
                      <div class="declaration">
                        <h4>Declaration</h4>
                        <div class="language">
                          <p class="aside-title">Swift</p>
                          <pre class="highlight swift"><code><span class="kd">public</span> <span class="kd">func</span> <span class="nf">greatestCommonDivisor</span><span class="p">(</span><span class="n">with</span> <span class="nv">b</span><span class="p">:</span> <span class="kt">BigInt</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="kt">BigInt</span></code></pre>

                        </div>
                      </div>
                      <div class="slightly-smaller">
                        <a href="https://github.com/attaswift/tree/v5.2.1/Sources/GCD.swift#L64-L66">Show on GitHub</a>
                      </div>
                    </section>
                  </div>
                </li>
                <li class="item">
                  <div>
                    <code>
                    <a name="/s:6BigIntAAV7inverseyABSgABF"></a>
                    <a name="//apple_ref/swift/Method/inverse(_:)" class="dashAnchor"></a>
                    <a class="token" href="#/s:6BigIntAAV7inverseyABSgABF">inverse(_:<wbr>)</a>
                    </code>
                  </div>
                  <div class="height-container">
                    <div class="pointer-container"></div>
                    <section class="section">
                      <div class="pointer"></div>
                      <div class="abstract">
                        <p>Returns the <a href="https://en.wikipedia.org/wiki/Extended_Euclidean_algorithm#Modular_integers">multiplicative inverse of this integer in modulo <code>modulus</code> arithmetic</a>,
or <code>nil</code> if there is no such number.</p>
<div class="aside aside-requires">
    <p class="aside-title">Requires</p>
    modulus.magnitude &gt; 1

</div><div class="aside aside-complexity">
    <p class="aside-title">Complexity</p>
    O(count^3)

</div>

                      </div>
                      <div class="declaration">
                        <h4>Declaration</h4>
                        <div class="language">
                          <p class="aside-title">Swift</p>
                          <pre class="highlight swift"><code><span class="kd">public</span> <span class="kd">func</span> <span class="nf">inverse</span><span class="p">(</span><span class="n">_</span> <span class="nv">modulus</span><span class="p">:</span> <span class="kt">BigInt</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="kt">BigInt</span><span class="p">?</span></code></pre>

                        </div>
                      </div>
                      <div>
                        <h4>Return Value</h4>
                        <p>If <code>gcd(self, modulus) == 1</code>, the value returned is an integer <code>a &lt; modulus</code> such that <code>(a * self) % modulus == 1</code>. If <code>self</code> and <code>modulus</code> aren&rsquo;t coprime, the return value is <code>nil</code>.</p>
                      </div>
                      <div class="slightly-smaller">
                        <a href="https://github.com/attaswift/tree/v5.2.1/Sources/GCD.swift#L76-L79">Show on GitHub</a>
                      </div>
                    </section>
                  </div>
                </li>
                <li class="item">
                  <div>
                    <code>
                    <a name="/s:6BigIntAAV4hash4intoys6HasherVz_tF"></a>
                    <a name="//apple_ref/swift/Method/hash(into:)" class="dashAnchor"></a>
                    <a class="token" href="#/s:6BigIntAAV4hash4intoys6HasherVz_tF">hash(into:<wbr>)</a>
                    </code>
                  </div>
                  <div class="height-container">
                    <div class="pointer-container"></div>
                    <section class="section">
                      <div class="pointer"></div>
                      <div class="abstract">
                        <p>Append this <code>BigInt</code> to the specified hasher.</p>

                      </div>
                      <div class="declaration">
                        <h4>Declaration</h4>
                        <div class="language">
                          <p class="aside-title">Swift</p>
                          <pre class="highlight swift"><code><span class="kd">public</span> <span class="kd">func</span> <span class="nf">hash</span><span class="p">(</span><span class="n">into</span> <span class="nv">hasher</span><span class="p">:</span> <span class="k">inout</span> <span class="kt">Hasher</span><span class="p">)</span></code></pre>

                        </div>
                      </div>
                      <div class="slightly-smaller">
                        <a href="https://github.com/attaswift/tree/v5.2.1/Sources/Hashable.swift#L22-L25">Show on GitHub</a>
                      </div>
                    </section>
                  </div>
                </li>
                <li class="item">
                  <div>
                    <code>
                    <a name="/s:6BigIntAAVABycfc"></a>
                    <a name="//apple_ref/swift/Method/init()" class="dashAnchor"></a>
                    <a class="token" href="#/s:6BigIntAAVABycfc">init()</a>
                    </code>
                  </div>
                  <div class="height-container">
                    <div class="pointer-container"></div>
                    <section class="section">
                      <div class="pointer"></div>
                      <div class="abstract">
                        <p>Undocumented</p>

                      </div>
                      <div class="declaration">
                        <h4>Declaration</h4>
                        <div class="language">
                          <p class="aside-title">Swift</p>
                          <pre class="highlight swift"><code><span class="kd">public</span> <span class="nf">init</span><span class="p">()</span></code></pre>

                        </div>
                      </div>
                      <div class="slightly-smaller">
                        <a href="https://github.com/attaswift/tree/v5.2.1/Sources/Integer Conversion.swift#L42-L44">Show on GitHub</a>
                      </div>
                    </section>
                  </div>
                </li>
                <li class="item">
                  <div>
                    <code>
                    <a name="/s:6BigIntAAVyAbA0A4UIntVcfc"></a>
                    <a name="//apple_ref/swift/Method/init(_:)" class="dashAnchor"></a>
                    <a class="token" href="#/s:6BigIntAAVyAbA0A4UIntVcfc">init(_:<wbr>)</a>
                    </code>
                  </div>
                  <div class="height-container">
                    <div class="pointer-container"></div>
                    <section class="section">
                      <div class="pointer"></div>
                      <div class="abstract">
                        <p>Initializes a new signed big integer with the same value as the specified unsigned big integer.</p>

                      </div>
                      <div class="declaration">
                        <h4>Declaration</h4>
                        <div class="language">
                          <p class="aside-title">Swift</p>
                          <pre class="highlight swift"><code><span class="kd">public</span> <span class="nf">init</span><span class="p">(</span><span class="n">_</span> <span class="nv">integer</span><span class="p">:</span> <span class="kt"><a href="../Structs/BigUInt.html">BigUInt</a></span><span class="p">)</span></code></pre>

                        </div>
                      </div>
                      <div class="slightly-smaller">
                        <a href="https://github.com/attaswift/tree/v5.2.1/Sources/Integer Conversion.swift#L47-L50">Show on GitHub</a>
                      </div>
                    </section>
                  </div>
                </li>
                <li class="item">
                  <div>
                    <code>
                    <a name="/s:Szyxqd__cSzRd__lufc"></a>
                    <a name="//apple_ref/swift/Method/init(_:)" class="dashAnchor"></a>
                    <a class="token" href="#/s:Szyxqd__cSzRd__lufc">init(_:<wbr>)</a>
                    </code>
                  </div>
                  <div class="height-container">
                    <div class="pointer-container"></div>
                    <section class="section">
                      <div class="pointer"></div>
                      <div class="abstract">
                        
                      </div>
                      <div class="declaration">
                        <h4>Declaration</h4>
                        <div class="language">
                          <p class="aside-title">Swift</p>
                          <pre class="highlight swift"><code><span class="kd">public</span> <span class="kd">init</span><span class="o">&lt;</span><span class="kt">T</span><span class="o">&gt;</span><span class="p">(</span><span class="n">_</span> <span class="nv">source</span><span class="p">:</span> <span class="kt">T</span><span class="p">)</span> <span class="k">where</span> <span class="kt">T</span> <span class="p">:</span> <span class="kt">BinaryInteger</span></code></pre>

                        </div>
                      </div>
                      <div class="slightly-smaller">
                        <a href="https://github.com/attaswift/tree/v5.2.1/Sources/Integer Conversion.swift#L52-L61">Show on GitHub</a>
                      </div>
                    </section>
                  </div>
                </li>
                <li class="item">
                  <div>
                    <code>
                    <a name="/s:Sj7exactlyxSgqd___tcSzRd__lufc"></a>
                    <a name="//apple_ref/swift/Method/init(exactly:)" class="dashAnchor"></a>
                    <a class="token" href="#/s:Sj7exactlyxSgqd___tcSzRd__lufc">init(exactly:<wbr>)</a>
                    </code>
                  </div>
                  <div class="height-container">
                    <div class="pointer-container"></div>
                    <section class="section">
                      <div class="pointer"></div>
                      <div class="abstract">
                        
                      </div>
                      <div class="declaration">
                        <h4>Declaration</h4>
                        <div class="language">
                          <p class="aside-title">Swift</p>
                          <pre class="highlight swift"><code><span class="kd">public</span> <span class="kd">init</span><span class="p">?</span><span class="o">&lt;</span><span class="kt">T</span><span class="o">&gt;</span><span class="p">(</span><span class="n">exactly</span> <span class="nv">source</span><span class="p">:</span> <span class="kt">T</span><span class="p">)</span> <span class="k">where</span> <span class="kt">T</span> <span class="p">:</span> <span class="kt">BinaryInteger</span></code></pre>

                        </div>
                      </div>
                      <div class="slightly-smaller">
                        <a href="https://github.com/attaswift/tree/v5.2.1/Sources/Integer Conversion.swift#L63-L65">Show on GitHub</a>
                      </div>
                    </section>
                  </div>
                </li>
                <li class="item">
                  <div>
                    <code>
                    <a name="/s:Sz8clampingxqd___tcSzRd__lufc"></a>
                    <a name="//apple_ref/swift/Method/init(clamping:)" class="dashAnchor"></a>
                    <a class="token" href="#/s:Sz8clampingxqd___tcSzRd__lufc">init(clamping:<wbr>)</a>
                    </code>
                  </div>
                  <div class="height-container">
                    <div class="pointer-container"></div>
                    <section class="section">
                      <div class="pointer"></div>
                      <div class="abstract">
                        
                      </div>
                      <div class="declaration">
                        <h4>Declaration</h4>
                        <div class="language">
                          <p class="aside-title">Swift</p>
                          <pre class="highlight swift"><code><span class="kd">public</span> <span class="kd">init</span><span class="o">&lt;</span><span class="kt">T</span><span class="o">&gt;</span><span class="p">(</span><span class="n">clamping</span> <span class="nv">source</span><span class="p">:</span> <span class="kt">T</span><span class="p">)</span> <span class="k">where</span> <span class="kt">T</span> <span class="p">:</span> <span class="kt">BinaryInteger</span></code></pre>

                        </div>
                      </div>
                      <div class="slightly-smaller">
                        <a href="https://github.com/attaswift/tree/v5.2.1/Sources/Integer Conversion.swift#L67-L69">Show on GitHub</a>
                      </div>
                    </section>
                  </div>
                </li>
                <li class="item">
                  <div>
                    <code>
                    <a name="/s:Sz18truncatingIfNeededxqd___tcSzRd__lufc"></a>
                    <a name="//apple_ref/swift/Method/init(truncatingIfNeeded:)" class="dashAnchor"></a>
                    <a class="token" href="#/s:Sz18truncatingIfNeededxqd___tcSzRd__lufc">init(truncatingIfNeeded:<wbr>)</a>
                    </code>
                  </div>
                  <div class="height-container">
                    <div class="pointer-container"></div>
                    <section class="section">
                      <div class="pointer"></div>
                      <div class="abstract">
                        
                      </div>
                      <div class="declaration">
                        <h4>Declaration</h4>
                        <div class="language">
                          <p class="aside-title">Swift</p>
                          <pre class="highlight swift"><code><span class="kd">public</span> <span class="kd">init</span><span class="o">&lt;</span><span class="kt">T</span><span class="o">&gt;</span><span class="p">(</span><span class="n">truncatingIfNeeded</span> <span class="nv">source</span><span class="p">:</span> <span class="kt">T</span><span class="p">)</span> <span class="k">where</span> <span class="kt">T</span> <span class="p">:</span> <span class="kt">BinaryInteger</span></code></pre>

                        </div>
                      </div>
                      <div class="slightly-smaller">
                        <a href="https://github.com/attaswift/tree/v5.2.1/Sources/Integer Conversion.swift#L71-L73">Show on GitHub</a>
                      </div>
                    </section>
                  </div>
                </li>
                <li class="item">
                  <div>
                    <code>
                    <a name="/s:6BigIntAAV14integerLiteralABs5Int64V_tcfc"></a>
                    <a name="//apple_ref/swift/Method/init(integerLiteral:)" class="dashAnchor"></a>
                    <a class="token" href="#/s:6BigIntAAV14integerLiteralABs5Int64V_tcfc">init(integerLiteral:<wbr>)</a>
                    </code>
                  </div>
                  <div class="height-container">
                    <div class="pointer-container"></div>
                    <section class="section">
                      <div class="pointer"></div>
                      <div class="abstract">
                        <p>Initialize a new big integer from an integer literal.</p>

                      </div>
                      <div class="declaration">
                        <h4>Declaration</h4>
                        <div class="language">
                          <p class="aside-title">Swift</p>
                          <pre class="highlight swift"><code><span class="kd">public</span> <span class="nf">init</span><span class="p">(</span><span class="n">integerLiteral</span> <span class="nv">value</span><span class="p">:</span> <span class="kt">Int64</span><span class="p">)</span></code></pre>

                        </div>
                      </div>
                      <div class="slightly-smaller">
                        <a href="https://github.com/attaswift/tree/v5.2.1/Sources/Integer Conversion.swift#L85-L87">Show on GitHub</a>
                      </div>
                    </section>
                  </div>
                </li>
                <li class="item">
                  <div>
                    <code>
                    <a name="/s:6BigIntAAV1moiyA2B_ABtFZ"></a>
                    <a name="//apple_ref/swift/Method/*(_:_:)" class="dashAnchor"></a>
                    <a class="token" href="#/s:6BigIntAAV1moiyA2B_ABtFZ">*(_:<wbr>_:<wbr>)</a>
                    </code>
                  </div>
                  <div class="height-container">
                    <div class="pointer-container"></div>
                    <section class="section">
                      <div class="pointer"></div>
                      <div class="abstract">
                        <p>Multiply <code>a</code> with <code>b</code> and return the result.</p>

                      </div>
                      <div class="declaration">
                        <h4>Declaration</h4>
                        <div class="language">
                          <p class="aside-title">Swift</p>
                          <pre class="highlight swift"><code><span class="kd">public</span> <span class="kd">static</span> <span class="kd">func</span> <span class="o">*</span> <span class="p">(</span><span class="nv">a</span><span class="p">:</span> <span class="kt">BigInt</span><span class="p">,</span> <span class="nv">b</span><span class="p">:</span> <span class="kt">BigInt</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="kt">BigInt</span></code></pre>

                        </div>
                      </div>
                      <div class="slightly-smaller">
                        <a href="https://github.com/attaswift/tree/v5.2.1/Sources/Multiplication.swift#L159-L161">Show on GitHub</a>
                      </div>
                    </section>
                  </div>
                </li>
                <li class="item">
                  <div>
                    <code>
                    <a name="/s:6BigIntAAV2meoiyyABz_ABtFZ"></a>
                    <a name="//apple_ref/swift/Method/*=(_:_:)" class="dashAnchor"></a>
                    <a class="token" href="#/s:6BigIntAAV2meoiyyABz_ABtFZ">*=(_:<wbr>_:<wbr>)</a>
                    </code>
                  </div>
                  <div class="height-container">
                    <div class="pointer-container"></div>
                    <section class="section">
                      <div class="pointer"></div>
                      <div class="abstract">
                        <p>Multiply <code>a</code> with <code>b</code> in place.</p>

                      </div>
                      <div class="declaration">
                        <h4>Declaration</h4>
                        <div class="language">
                          <p class="aside-title">Swift</p>
                          <pre class="highlight swift"><code><span class="kd">public</span> <span class="kd">static</span> <span class="kd">func</span> <span class="o">*=</span> <span class="p">(</span><span class="nv">a</span><span class="p">:</span> <span class="k">inout</span> <span class="kt">BigInt</span><span class="p">,</span> <span class="nv">b</span><span class="p">:</span> <span class="kt">BigInt</span><span class="p">)</span></code></pre>

                        </div>
                      </div>
                      <div class="slightly-smaller">
                        <a href="https://github.com/attaswift/tree/v5.2.1/Sources/Multiplication.swift#L164">Show on GitHub</a>
                      </div>
                    </section>
                  </div>
                </li>
              </ul>
            </div>
            <div class="task-group">
              <div class="task-name-container">
                <a name="/Primality%20Testing"></a>
                <a name="//apple_ref/swift/Section/Primality Testing" class="dashAnchor"></a>
                <div class="section-name-container">
                  <a class="section-name-link" href="#/Primality%20Testing"></a>
                  <h3 class="section-name"><p>Primality Testing</p>
</h3>
                </div>
              </div>
              <ul class="item-container">
                <li class="item">
                  <div>
                    <code>
                    <a name="/s:6BigIntAAV21isStrongProbablePrimeySbABF"></a>
                    <a name="//apple_ref/swift/Method/isStrongProbablePrime(_:)" class="dashAnchor"></a>
                    <a class="token" href="#/s:6BigIntAAV21isStrongProbablePrimeySbABF">isStrongProbablePrime(_:<wbr>)</a>
                    </code>
                  </div>
                  <div class="height-container">
                    <div class="pointer-container"></div>
                    <section class="section">
                      <div class="pointer"></div>
                      <div class="abstract">
                        <p>Returns true iff this integer passes the <a href="https://en.wikipedia.org/wiki/Probable_prime">strong probable prime test</a> for the specified base.</p>

                      </div>
                      <div class="declaration">
                        <h4>Declaration</h4>
                        <div class="language">
                          <p class="aside-title">Swift</p>
                          <pre class="highlight swift"><code><span class="kd">public</span> <span class="kd">func</span> <span class="nf">isStrongProbablePrime</span><span class="p">(</span><span class="n">_</span> <span class="nv">base</span><span class="p">:</span> <span class="kt">BigInt</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="kt">Bool</span></code></pre>

                        </div>
                      </div>
                      <div class="slightly-smaller">
                        <a href="https://github.com/attaswift/tree/v5.2.1/Sources/Prime Test.swift#L130-L134">Show on GitHub</a>
                      </div>
                    </section>
                  </div>
                </li>
                <li class="item">
                  <div>
                    <code>
                    <a name="/s:6BigIntAAV7isPrime6roundsSbSi_tF"></a>
                    <a name="//apple_ref/swift/Method/isPrime(rounds:)" class="dashAnchor"></a>
                    <a class="token" href="#/s:6BigIntAAV7isPrime6roundsSbSi_tF">isPrime(rounds:<wbr>)</a>
                    </code>
                  </div>
                  <div class="height-container">
                    <div class="pointer-container"></div>
                    <section class="section">
                      <div class="pointer"></div>
                      <div class="abstract">
                        <p>Returns true if this integer is probably prime. Returns false if this integer is definitely not prime.</p>

<p>This function performs a probabilistic <a href="https://en.wikipedia.org/wiki/Miller%E2%80%93Rabin_primality_test">Miller-Rabin Primality Test</a>, consisting of <code>rounds</code> iterations,
each calculating the strong probable prime test for a random base. The number of rounds is 10 by default,
but you may specify your own choice.</p>

<p>To speed things up, the function checks if <code>self</code> is divisible by the first few prime numbers before
diving into (slower) Miller-Rabin testing.</p>

<p>Also, when <code>self</code> is less than 82 bits wide, <code>isPrime</code> does a deterministic test that is guaranteed to
return a correct result.</p>

                      </div>
                      <div class="declaration">
                        <h4>Declaration</h4>
                        <div class="language">
                          <p class="aside-title">Swift</p>
                          <pre class="highlight swift"><code><span class="kd">public</span> <span class="kd">func</span> <span class="nf">isPrime</span><span class="p">(</span><span class="nv">rounds</span><span class="p">:</span> <span class="kt">Int</span> <span class="o">=</span> <span class="mi">10</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="kt">Bool</span></code></pre>

                        </div>
                      </div>
                      <div class="slightly-smaller">
                        <a href="https://github.com/attaswift/tree/v5.2.1/Sources/Prime Test.swift#L149-L152">Show on GitHub</a>
                      </div>
                    </section>
                  </div>
                </li>
                <li class="item">
                  <div>
                    <code>
                    <a name="/s:6BigIntAAV3alloiyA2B_ABtFZ"></a>
                    <a name="//apple_ref/swift/Method/&amp;&lt;&lt;(_:_:)" class="dashAnchor"></a>
                    <a class="token" href="#/s:6BigIntAAV3alloiyA2B_ABtFZ">&<<(_:<wbr>_:<wbr>)</a>
                    </code>
                  </div>
                  <div class="height-container">
                    <div class="pointer-container"></div>
                    <section class="section">
                      <div class="pointer"></div>
                      <div class="abstract">
                        <p>Undocumented</p>

                      </div>
                      <div class="declaration">
                        <h4>Declaration</h4>
                        <div class="language">
                          <p class="aside-title">Swift</p>
                          <pre class="highlight swift"><code><span class="kd">public</span> <span class="kd">static</span> <span class="kd">func</span> <span class="o">&amp;&lt;&lt;</span> <span class="p">(</span><span class="nv">left</span><span class="p">:</span> <span class="kt">BigInt</span><span class="p">,</span> <span class="nv">right</span><span class="p">:</span> <span class="kt">BigInt</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="kt">BigInt</span></code></pre>

                        </div>
                      </div>
                      <div class="slightly-smaller">
                        <a href="https://github.com/attaswift/tree/v5.2.1/Sources/Shifts.swift#L168-L170">Show on GitHub</a>
                      </div>
                    </section>
                  </div>
                </li>
                <li class="item">
                  <div>
                    <code>
                    <a name="/s:6BigIntAAV4alleoiyyABz_ABtFZ"></a>
                    <a name="//apple_ref/swift/Method/&amp;&lt;&lt;=(_:_:)" class="dashAnchor"></a>
                    <a class="token" href="#/s:6BigIntAAV4alleoiyyABz_ABtFZ">&<<=(_:<wbr>_:<wbr>)</a>
                    </code>
                  </div>
                  <div class="height-container">
                    <div class="pointer-container"></div>
                    <section class="section">
                      <div class="pointer"></div>
                      <div class="abstract">
                        <p>Undocumented</p>

                      </div>
                      <div class="declaration">
                        <h4>Declaration</h4>
                        <div class="language">
                          <p class="aside-title">Swift</p>
                          <pre class="highlight swift"><code><span class="kd">public</span> <span class="kd">static</span> <span class="kd">func</span> <span class="o">&amp;&lt;&lt;=</span> <span class="p">(</span><span class="nv">left</span><span class="p">:</span> <span class="k">inout</span> <span class="kt">BigInt</span><span class="p">,</span> <span class="nv">right</span><span class="p">:</span> <span class="kt">BigInt</span><span class="p">)</span></code></pre>

                        </div>
                      </div>
                      <div class="slightly-smaller">
                        <a href="https://github.com/attaswift/tree/v5.2.1/Sources/Shifts.swift#L172-L174">Show on GitHub</a>
                      </div>
                    </section>
                  </div>
                </li>
                <li class="item">
                  <div>
                    <code>
                    <a name="/s:6BigIntAAV3aggoiyA2B_ABtFZ"></a>
                    <a name="//apple_ref/swift/Method/&amp;&gt;&gt;(_:_:)" class="dashAnchor"></a>
                    <a class="token" href="#/s:6BigIntAAV3aggoiyA2B_ABtFZ">&>>(_:<wbr>_:<wbr>)</a>
                    </code>
                  </div>
                  <div class="height-container">
                    <div class="pointer-container"></div>
                    <section class="section">
                      <div class="pointer"></div>
                      <div class="abstract">
                        <p>Undocumented</p>

                      </div>
                      <div class="declaration">
                        <h4>Declaration</h4>
                        <div class="language">
                          <p class="aside-title">Swift</p>
                          <pre class="highlight swift"><code><span class="kd">public</span> <span class="kd">static</span> <span class="kd">func</span> <span class="o">&amp;&gt;&gt;</span> <span class="p">(</span><span class="nv">left</span><span class="p">:</span> <span class="kt">BigInt</span><span class="p">,</span> <span class="nv">right</span><span class="p">:</span> <span class="kt">BigInt</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="kt">BigInt</span></code></pre>

                        </div>
                      </div>
                      <div class="slightly-smaller">
                        <a href="https://github.com/attaswift/tree/v5.2.1/Sources/Shifts.swift#L176-L178">Show on GitHub</a>
                      </div>
                    </section>
                  </div>
                </li>
                <li class="item">
                  <div>
                    <code>
                    <a name="/s:6BigIntAAV4aggeoiyyABz_ABtFZ"></a>
                    <a name="//apple_ref/swift/Method/&amp;&gt;&gt;=(_:_:)" class="dashAnchor"></a>
                    <a class="token" href="#/s:6BigIntAAV4aggeoiyyABz_ABtFZ">&>>=(_:<wbr>_:<wbr>)</a>
                    </code>
                  </div>
                  <div class="height-container">
                    <div class="pointer-container"></div>
                    <section class="section">
                      <div class="pointer"></div>
                      <div class="abstract">
                        <p>Undocumented</p>

                      </div>
                      <div class="declaration">
                        <h4>Declaration</h4>
                        <div class="language">
                          <p class="aside-title">Swift</p>
                          <pre class="highlight swift"><code><span class="kd">public</span> <span class="kd">static</span> <span class="kd">func</span> <span class="o">&amp;&gt;&gt;=</span> <span class="p">(</span><span class="nv">left</span><span class="p">:</span> <span class="k">inout</span> <span class="kt">BigInt</span><span class="p">,</span> <span class="nv">right</span><span class="p">:</span> <span class="kt">BigInt</span><span class="p">)</span></code></pre>

                        </div>
                      </div>
                      <div class="slightly-smaller">
                        <a href="https://github.com/attaswift/tree/v5.2.1/Sources/Shifts.swift#L180-L182">Show on GitHub</a>
                      </div>
                    </section>
                  </div>
                </li>
                <li class="item">
                  <div>
                    <code>
                    <a name="/s:6BigIntAAV2lloiyA2B_xtSzRzlFZ"></a>
                    <a name="//apple_ref/swift/Method/&lt;&lt;(_:_:)" class="dashAnchor"></a>
                    <a class="token" href="#/s:6BigIntAAV2lloiyA2B_xtSzRzlFZ"><<(_:<wbr>_:<wbr>)</a>
                    </code>
                  </div>
                  <div class="height-container">
                    <div class="pointer-container"></div>
                    <section class="section">
                      <div class="pointer"></div>
                      <div class="abstract">
                        <p>Undocumented</p>

                      </div>
                      <div class="declaration">
                        <h4>Declaration</h4>
                        <div class="language">
                          <p class="aside-title">Swift</p>
                          <pre class="highlight swift"><code><span class="kd">public</span> <span class="kd">static</span> <span class="kd">func</span> <span class="o">&lt;&lt;</span> <span class="o">&lt;</span><span class="kt">Other</span><span class="o">&gt;</span><span class="p">(</span><span class="nv">lhs</span><span class="p">:</span> <span class="kt">BigInt</span><span class="p">,</span> <span class="nv">rhs</span><span class="p">:</span> <span class="kt">Other</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="kt">BigInt</span> <span class="k">where</span> <span class="kt">Other</span> <span class="p">:</span> <span class="kt">BinaryInteger</span></code></pre>

                        </div>
                      </div>
                      <div class="slightly-smaller">
                        <a href="https://github.com/attaswift/tree/v5.2.1/Sources/Shifts.swift#L184-L187">Show on GitHub</a>
                      </div>
                    </section>
                  </div>
                </li>
                <li class="item">
                  <div>
                    <code>
                    <a name="/s:6BigIntAAV3lleoiyyABz_xtSzRzlFZ"></a>
                    <a name="//apple_ref/swift/Method/&lt;&lt;=(_:_:)" class="dashAnchor"></a>
                    <a class="token" href="#/s:6BigIntAAV3lleoiyyABz_xtSzRzlFZ"><<=(_:<wbr>_:<wbr>)</a>
                    </code>
                  </div>
                  <div class="height-container">
                    <div class="pointer-container"></div>
                    <section class="section">
                      <div class="pointer"></div>
                      <div class="abstract">
                        <p>Undocumented</p>

                      </div>
                      <div class="declaration">
                        <h4>Declaration</h4>
                        <div class="language">
                          <p class="aside-title">Swift</p>
                          <pre class="highlight swift"><code><span class="kd">public</span> <span class="kd">static</span> <span class="kd">func</span> <span class="o">&lt;&lt;=</span> <span class="o">&lt;</span><span class="kt">Other</span><span class="o">&gt;</span><span class="p">(</span><span class="nv">lhs</span><span class="p">:</span> <span class="k">inout</span> <span class="kt">BigInt</span><span class="p">,</span> <span class="nv">rhs</span><span class="p">:</span> <span class="kt">Other</span><span class="p">)</span> <span class="k">where</span> <span class="kt">Other</span> <span class="p">:</span> <span class="kt">BinaryInteger</span></code></pre>

                        </div>
                      </div>
                      <div class="slightly-smaller">
                        <a href="https://github.com/attaswift/tree/v5.2.1/Sources/Shifts.swift#L189-L196">Show on GitHub</a>
                      </div>
                    </section>
                  </div>
                </li>
                <li class="item">
                  <div>
                    <code>
                    <a name="/s:6BigIntAAV2ggoiyA2B_xtSzRzlFZ"></a>
                    <a name="//apple_ref/swift/Method/&gt;&gt;(_:_:)" class="dashAnchor"></a>
                    <a class="token" href="#/s:6BigIntAAV2ggoiyA2B_xtSzRzlFZ">>>(_:<wbr>_:<wbr>)</a>
                    </code>
                  </div>
                  <div class="height-container">
                    <div class="pointer-container"></div>
                    <section class="section">
                      <div class="pointer"></div>
                      <div class="abstract">
                        <p>Undocumented</p>

                      </div>
                      <div class="declaration">
                        <h4>Declaration</h4>
                        <div class="language">
                          <p class="aside-title">Swift</p>
                          <pre class="highlight swift"><code><span class="kd">public</span> <span class="kd">static</span> <span class="kd">func</span> <span class="o">&gt;&gt;</span> <span class="o">&lt;</span><span class="kt">Other</span><span class="o">&gt;</span><span class="p">(</span><span class="nv">lhs</span><span class="p">:</span> <span class="kt">BigInt</span><span class="p">,</span> <span class="nv">rhs</span><span class="p">:</span> <span class="kt">Other</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="kt">BigInt</span> <span class="k">where</span> <span class="kt">Other</span> <span class="p">:</span> <span class="kt">BinaryInteger</span></code></pre>

                        </div>
                      </div>
                      <div class="slightly-smaller">
                        <a href="https://github.com/attaswift/tree/v5.2.1/Sources/Shifts.swift#L198-L201">Show on GitHub</a>
                      </div>
                    </section>
                  </div>
                </li>
                <li class="item">
                  <div>
                    <code>
                    <a name="/s:6BigIntAAV3ggeoiyyABz_xtSzRzlFZ"></a>
                    <a name="//apple_ref/swift/Method/&gt;&gt;=(_:_:)" class="dashAnchor"></a>
                    <a class="token" href="#/s:6BigIntAAV3ggeoiyyABz_xtSzRzlFZ">>>=(_:<wbr>_:<wbr>)</a>
                    </code>
                  </div>
                  <div class="height-container">
                    <div class="pointer-container"></div>
                    <section class="section">
                      <div class="pointer"></div>
                      <div class="abstract">
                        <p>Undocumented</p>

                      </div>
                      <div class="declaration">
                        <h4>Declaration</h4>
                        <div class="language">
                          <p class="aside-title">Swift</p>
                          <pre class="highlight swift"><code><span class="kd">public</span> <span class="kd">static</span> <span class="kd">func</span> <span class="o">&gt;&gt;=</span> <span class="o">&lt;</span><span class="kt">Other</span><span class="o">&gt;</span><span class="p">(</span><span class="nv">lhs</span><span class="p">:</span> <span class="k">inout</span> <span class="kt">BigInt</span><span class="p">,</span> <span class="nv">rhs</span><span class="p">:</span> <span class="kt">Other</span><span class="p">)</span> <span class="k">where</span> <span class="kt">Other</span> <span class="p">:</span> <span class="kt">BinaryInteger</span></code></pre>

                        </div>
                      </div>
                      <div class="slightly-smaller">
                        <a href="https://github.com/attaswift/tree/v5.2.1/Sources/Shifts.swift#L203-L210">Show on GitHub</a>
                      </div>
                    </section>
                  </div>
                </li>
              </ul>
            </div>
            <div class="task-group">
              <div class="task-name-container">
                <a name="/Square%20Root"></a>
                <a name="//apple_ref/swift/Section/Square Root" class="dashAnchor"></a>
                <div class="section-name-container">
                  <a class="section-name-link" href="#/Square%20Root"></a>
                  <h3 class="section-name"><p>Square Root</p>
</h3>
                </div>
              </div>
              <ul class="item-container">
                <li class="item">
                  <div>
                    <code>
                    <a name="/s:6BigIntAAV10squareRootAByF"></a>
                    <a name="//apple_ref/swift/Method/squareRoot()" class="dashAnchor"></a>
                    <a class="token" href="#/s:6BigIntAAV10squareRootAByF">squareRoot()</a>
                    </code>
                  </div>
                  <div class="height-container">
                    <div class="pointer-container"></div>
                    <section class="section">
                      <div class="pointer"></div>
                      <div class="abstract">
                        <p>Returns the integer square root of a big integer; i.e., the largest integer whose square isn&rsquo;t greater than <code>value</code>.</p>
<div class="aside aside-requires">
    <p class="aside-title">Requires</p>
    self &gt;= 0

</div>

                      </div>
                      <div class="declaration">
                        <h4>Declaration</h4>
                        <div class="language">
                          <p class="aside-title">Swift</p>
                          <pre class="highlight swift"><code><span class="kd">public</span> <span class="kd">func</span> <span class="nf">squareRoot</span><span class="p">()</span> <span class="o">-&gt;</span> <span class="kt">BigInt</span></code></pre>

                        </div>
                      </div>
                      <div>
                        <h4>Return Value</h4>
                        <p>floor(sqrt(self))</p>
                      </div>
                      <div class="slightly-smaller">
                        <a href="https://github.com/attaswift/tree/v5.2.1/Sources/Square Root.swift#L37-L40">Show on GitHub</a>
                      </div>
                    </section>
                  </div>
                </li>
                <li class="item">
                  <div>
                    <code>
                    <a name="/s:Sx6StrideQa"></a>
                    <a name="//apple_ref/swift/Alias/Stride" class="dashAnchor"></a>
                    <a class="token" href="#/s:Sx6StrideQa">Stride</a>
                    </code>
                  </div>
                  <div class="height-container">
                    <div class="pointer-container"></div>
                    <section class="section">
                      <div class="pointer"></div>
                      <div class="abstract">
                        
                      </div>
                      <div class="declaration">
                        <h4>Declaration</h4>
                        <div class="language">
                          <p class="aside-title">Swift</p>
                          <pre class="highlight swift"><code><span class="kd">public</span> <span class="kd">typealias</span> <span class="kt">Stride</span> <span class="o">=</span> <span class="kt">BigInt</span></code></pre>

                        </div>
                      </div>
                      <div class="slightly-smaller">
                        <a href="https://github.com/attaswift/tree/v5.2.1/Sources/Strideable.swift#L">Show on GitHub</a>
                      </div>
                    </section>
                  </div>
                </li>
                <li class="item">
                  <div>
                    <code>
                    <a name="/s:6BigIntAAV8advanced2byA2B_tF"></a>
                    <a name="//apple_ref/swift/Method/advanced(by:)" class="dashAnchor"></a>
                    <a class="token" href="#/s:6BigIntAAV8advanced2byA2B_tF">advanced(by:<wbr>)</a>
                    </code>
                  </div>
                  <div class="height-container">
                    <div class="pointer-container"></div>
                    <section class="section">
                      <div class="pointer"></div>
                      <div class="abstract">
                        <p>Returns <code>self + n</code>.</p>

                      </div>
                      <div class="declaration">
                        <h4>Declaration</h4>
                        <div class="language">
                          <p class="aside-title">Swift</p>
                          <pre class="highlight swift"><code><span class="kd">public</span> <span class="kd">func</span> <span class="nf">advanced</span><span class="p">(</span><span class="n">by</span> <span class="nv">n</span><span class="p">:</span> <span class="kt"><a href="../Structs/BigInt.html#/s:Sx6StrideQa">Stride</a></span><span class="p">)</span> <span class="o">-&gt;</span> <span class="kt">BigInt</span></code></pre>

                        </div>
                      </div>
                      <div class="slightly-smaller">
                        <a href="https://github.com/attaswift/tree/v5.2.1/Sources/Strideable.swift#L28-L30">Show on GitHub</a>
                      </div>
                    </section>
                  </div>
                </li>
                <li class="item">
                  <div>
                    <code>
                    <a name="/s:6BigIntAAV8distance2toA2B_tF"></a>
                    <a name="//apple_ref/swift/Method/distance(to:)" class="dashAnchor"></a>
                    <a class="token" href="#/s:6BigIntAAV8distance2toA2B_tF">distance(to:<wbr>)</a>
                    </code>
                  </div>
                  <div class="height-container">
                    <div class="pointer-container"></div>
                    <section class="section">
                      <div class="pointer"></div>
                      <div class="abstract">
                        <p>Returns <code>other - self</code>.</p>

                      </div>
                      <div class="declaration">
                        <h4>Declaration</h4>
                        <div class="language">
                          <p class="aside-title">Swift</p>
                          <pre class="highlight swift"><code><span class="kd">public</span> <span class="kd">func</span> <span class="nf">distance</span><span class="p">(</span><span class="n">to</span> <span class="nv">other</span><span class="p">:</span> <span class="kt">BigInt</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="kt"><a href="../Structs/BigInt.html#/s:Sx6StrideQa">Stride</a></span></code></pre>

                        </div>
                      </div>
                      <div class="slightly-smaller">
                        <a href="https://github.com/attaswift/tree/v5.2.1/Sources/Strideable.swift#L33-L35">Show on GitHub</a>
                      </div>
                    </section>
                  </div>
                </li>
                <li class="item">
                  <div>
                    <code>
                    <a name="/s:6BigIntAAV_5radixABSgx_SitcSyRzlufc"></a>
                    <a name="//apple_ref/swift/Method/init(_:radix:)" class="dashAnchor"></a>
                    <a class="token" href="#/s:6BigIntAAV_5radixABSgx_SitcSyRzlufc">init(_:<wbr>radix:<wbr>)</a>
                    </code>
                  </div>
                  <div class="height-container">
                    <div class="pointer-container"></div>
                    <section class="section">
                      <div class="pointer"></div>
                      <div class="abstract">
                        <p>Initialize a big integer from an ASCII representation in a given radix. Numerals above <code>9</code> are represented by
letters from the English alphabet.</p>
<div class="aside aside-requires">
    <p class="aside-title">Requires</p>
    <code>radix &gt; 1 &amp;&amp; radix &lt; 36</code>

</div>

                      </div>
                      <div class="declaration">
                        <h4>Declaration</h4>
                        <div class="language">
                          <p class="aside-title">Swift</p>
                          <pre class="highlight swift"><code><span class="kd">public</span> <span class="kd">init</span><span class="p">?</span><span class="o">&lt;</span><span class="kt">S</span><span class="o">&gt;</span><span class="p">(</span><span class="n">_</span> <span class="nv">text</span><span class="p">:</span> <span class="kt">S</span><span class="p">,</span> <span class="nv">radix</span><span class="p">:</span> <span class="kt">Int</span> <span class="o">=</span> <span class="mi">10</span><span class="p">)</span> <span class="k">where</span> <span class="kt">S</span> <span class="p">:</span> <span class="kt">StringProtocol</span></code></pre>

                        </div>
                      </div>
                      <div>
                        <h4>Return Value</h4>
                        <p>The integer represented by <code>text</code>, or nil if <code>text</code> contains a character that does not represent a numeral in <code>radix</code>.</p>
                      </div>
                      <div class="slightly-smaller">
                        <a href="https://github.com/attaswift/tree/v5.2.1/Sources/String Conversion.swift#L83-L101">Show on GitHub</a>
                      </div>
                    </section>
                  </div>
                </li>
                <li class="item">
                  <div>
                    <code>
                    <a name="/s:6BigIntAAV20unicodeScalarLiteralABs7UnicodeO0D0V_tcfc"></a>
                    <a name="//apple_ref/swift/Method/init(unicodeScalarLiteral:)" class="dashAnchor"></a>
                    <a class="token" href="#/s:6BigIntAAV20unicodeScalarLiteralABs7UnicodeO0D0V_tcfc">init(unicodeScalarLiteral:<wbr>)</a>
                    </code>
                  </div>
                  <div class="height-container">
                    <div class="pointer-container"></div>
                    <section class="section">
                      <div class="pointer"></div>
                      <div class="abstract">
                        <p>Initialize a new big integer from a Unicode scalar.
The scalar must represent a decimal digit.</p>

                      </div>
                      <div class="declaration">
                        <h4>Declaration</h4>
                        <div class="language">
                          <p class="aside-title">Swift</p>
                          <pre class="highlight swift"><code><span class="kd">public</span> <span class="nf">init</span><span class="p">(</span><span class="n">unicodeScalarLiteral</span> <span class="nv">value</span><span class="p">:</span> <span class="kt">UnicodeScalar</span><span class="p">)</span></code></pre>

                        </div>
                      </div>
                      <div class="slightly-smaller">
                        <a href="https://github.com/attaswift/tree/v5.2.1/Sources/String Conversion.swift#L189-L191">Show on GitHub</a>
                      </div>
                    </section>
                  </div>
                </li>
                <li class="item">
                  <div>
                    <code>
                    <a name="/s:6BigIntAAV30extendedGraphemeClusterLiteralABSS_tcfc"></a>
                    <a name="//apple_ref/swift/Method/init(extendedGraphemeClusterLiteral:)" class="dashAnchor"></a>
                    <a class="token" href="#/s:6BigIntAAV30extendedGraphemeClusterLiteralABSS_tcfc">init(extendedGraphemeClusterLiteral:<wbr>)</a>
                    </code>
                  </div>
                  <div class="height-container">
                    <div class="pointer-container"></div>
                    <section class="section">
                      <div class="pointer"></div>
                      <div class="abstract">
                        <p>Initialize a new big integer from an extended grapheme cluster.
The cluster must consist of a decimal digit.</p>

                      </div>
                      <div class="declaration">
                        <h4>Declaration</h4>
                        <div class="language">
                          <p class="aside-title">Swift</p>
                          <pre class="highlight swift"><code><span class="kd">public</span> <span class="nf">init</span><span class="p">(</span><span class="n">extendedGraphemeClusterLiteral</span> <span class="nv">value</span><span class="p">:</span> <span class="kt">String</span><span class="p">)</span></code></pre>

                        </div>
                      </div>
                      <div class="slightly-smaller">
                        <a href="https://github.com/attaswift/tree/v5.2.1/Sources/String Conversion.swift#L195-L197">Show on GitHub</a>
                      </div>
                    </section>
                  </div>
                </li>
                <li class="item">
                  <div>
                    <code>
                    <a name="/s:6BigIntAAV13stringLiteralABSS_tcfc"></a>
                    <a name="//apple_ref/swift/Method/init(stringLiteral:)" class="dashAnchor"></a>
                    <a class="token" href="#/s:6BigIntAAV13stringLiteralABSS_tcfc">init(stringLiteral:<wbr>)</a>
                    </code>
                  </div>
                  <div class="height-container">
                    <div class="pointer-container"></div>
                    <section class="section">
                      <div class="pointer"></div>
                      <div class="abstract">
                        <p>Initialize a new big integer from a decimal number represented by a string literal of arbitrary length.
The string must contain only decimal digits.</p>

                      </div>
                      <div class="declaration">
                        <h4>Declaration</h4>
                        <div class="language">
                          <p class="aside-title">Swift</p>
                          <pre class="highlight swift"><code><span class="kd">public</span> <span class="nf">init</span><span class="p">(</span><span class="n">stringLiteral</span> <span class="nv">value</span><span class="p">:</span> <span class="kt">StringLiteralType</span><span class="p">)</span></code></pre>

                        </div>
                      </div>
                      <div class="slightly-smaller">
                        <a href="https://github.com/attaswift/tree/v5.2.1/Sources/String Conversion.swift#L201-L203">Show on GitHub</a>
                      </div>
                    </section>
                  </div>
                </li>
                <li class="item">
                  <div>
                    <code>
                    <a name="/s:6BigIntAAV11descriptionSSvp"></a>
                    <a name="//apple_ref/swift/Property/description" class="dashAnchor"></a>
                    <a class="token" href="#/s:6BigIntAAV11descriptionSSvp">description</a>
                    </code>
                  </div>
                  <div class="height-container">
                    <div class="pointer-container"></div>
                    <section class="section">
                      <div class="pointer"></div>
                      <div class="abstract">
                        <p>Return the decimal representation of this integer.</p>

                      </div>
                      <div class="declaration">
                        <h4>Declaration</h4>
                        <div class="language">
                          <p class="aside-title">Swift</p>
                          <pre class="highlight swift"><code><span class="kd">public</span> <span class="k">var</span> <span class="nv">description</span><span class="p">:</span> <span class="kt">String</span> <span class="p">{</span> <span class="k">get</span> <span class="p">}</span></code></pre>

                        </div>
                      </div>
                      <div class="slightly-smaller">
                        <a href="https://github.com/attaswift/tree/v5.2.1/Sources/String Conversion.swift#L215-L217">Show on GitHub</a>
                      </div>
                    </section>
                  </div>
                </li>
                <li class="item">
                  <div>
                    <code>
                    <a name="/s:6BigIntAAV21playgroundDescriptionypvp"></a>
                    <a name="//apple_ref/swift/Property/playgroundDescription" class="dashAnchor"></a>
                    <a class="token" href="#/s:6BigIntAAV21playgroundDescriptionypvp">playgroundDescription</a>
                    </code>
                  </div>
                  <div class="height-container">
                    <div class="pointer-container"></div>
                    <section class="section">
                      <div class="pointer"></div>
                      <div class="abstract">
                        <p>Return the playground quick look representation of this integer.</p>

                      </div>
                      <div class="declaration">
                        <h4>Declaration</h4>
                        <div class="language">
                          <p class="aside-title">Swift</p>
                          <pre class="highlight swift"><code><span class="kd">public</span> <span class="k">var</span> <span class="nv">playgroundDescription</span><span class="p">:</span> <span class="kt">Any</span> <span class="p">{</span> <span class="k">get</span> <span class="p">}</span></code></pre>

                        </div>
                      </div>
                      <div class="slightly-smaller">
                        <a href="https://github.com/attaswift/tree/v5.2.1/Sources/String Conversion.swift#L232-L235">Show on GitHub</a>
                      </div>
                    </section>
                  </div>
                </li>
                <li class="item">
                  <div>
                    <code>
                    <a name="/s:6BigIntAAV6negateyyF"></a>
                    <a name="//apple_ref/swift/Method/negate()" class="dashAnchor"></a>
                    <a class="token" href="#/s:6BigIntAAV6negateyyF">negate()</a>
                    </code>
                  </div>
                  <div class="height-container">
                    <div class="pointer-container"></div>
                    <section class="section">
                      <div class="pointer"></div>
                      <div class="abstract">
                        <p>Undocumented</p>

                      </div>
                      <div class="declaration">
                        <h4>Declaration</h4>
                        <div class="language">
                          <p class="aside-title">Swift</p>
                          <pre class="highlight swift"><code><span class="kd">public</span> <span class="k">mutating</span> <span class="kd">func</span> <span class="nf">negate</span><span class="p">()</span></code></pre>

                        </div>
                      </div>
                      <div class="slightly-smaller">
                        <a href="https://github.com/attaswift/tree/v5.2.1/Sources/Subtraction.swift#L157-L160">Show on GitHub</a>
                      </div>
                    </section>
                  </div>
                </li>
                <li class="item">
                  <div>
                    <code>
                    <a name="/s:6BigIntAAV1soiyA2B_ABtFZ"></a>
                    <a name="//apple_ref/swift/Method/-(_:_:)" class="dashAnchor"></a>
                    <a class="token" href="#/s:6BigIntAAV1soiyA2B_ABtFZ">-(_:<wbr>_:<wbr>)</a>
                    </code>
                  </div>
                  <div class="height-container">
                    <div class="pointer-container"></div>
                    <section class="section">
                      <div class="pointer"></div>
                      <div class="abstract">
                        <p>Subtract <code>b</code> from <code>a</code> and return the result.</p>

                      </div>
                      <div class="declaration">
                        <h4>Declaration</h4>
                        <div class="language">
                          <p class="aside-title">Swift</p>
                          <pre class="highlight swift"><code><span class="kd">public</span> <span class="kd">static</span> <span class="kd">func</span> <span class="o">-</span> <span class="p">(</span><span class="nv">a</span><span class="p">:</span> <span class="kt">BigInt</span><span class="p">,</span> <span class="nv">b</span><span class="p">:</span> <span class="kt">BigInt</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="kt">BigInt</span></code></pre>

                        </div>
                      </div>
                      <div class="slightly-smaller">
                        <a href="https://github.com/attaswift/tree/v5.2.1/Sources/Subtraction.swift#L163-L165">Show on GitHub</a>
                      </div>
                    </section>
                  </div>
                </li>
                <li class="item">
                  <div>
                    <code>
                    <a name="/s:6BigIntAAV2seoiyyABz_ABtFZ"></a>
                    <a name="//apple_ref/swift/Method/-=(_:_:)" class="dashAnchor"></a>
                    <a class="token" href="#/s:6BigIntAAV2seoiyyABz_ABtFZ">-=(_:<wbr>_:<wbr>)</a>
                    </code>
                  </div>
                  <div class="height-container">
                    <div class="pointer-container"></div>
                    <section class="section">
                      <div class="pointer"></div>
                      <div class="abstract">
                        <p>Subtract <code>b</code> from <code>a</code> in place.</p>

                      </div>
                      <div class="declaration">
                        <h4>Declaration</h4>
                        <div class="language">
                          <p class="aside-title">Swift</p>
                          <pre class="highlight swift"><code><span class="kd">public</span> <span class="kd">static</span> <span class="kd">func</span> <span class="o">-=</span> <span class="p">(</span><span class="nv">a</span><span class="p">:</span> <span class="k">inout</span> <span class="kt">BigInt</span><span class="p">,</span> <span class="nv">b</span><span class="p">:</span> <span class="kt">BigInt</span><span class="p">)</span></code></pre>

                        </div>
                      </div>
                      <div class="slightly-smaller">
                        <a href="https://github.com/attaswift/tree/v5.2.1/Sources/Subtraction.swift#L168">Show on GitHub</a>
                      </div>
                    </section>
                  </div>
                </li>
                <li class="item">
                  <div>
                    <code>
                    <a name="/s:6BigIntAAV8bitWidthSivp"></a>
                    <a name="//apple_ref/swift/Property/bitWidth" class="dashAnchor"></a>
                    <a class="token" href="#/s:6BigIntAAV8bitWidthSivp">bitWidth</a>
                    </code>
                  </div>
                  <div class="height-container">
                    <div class="pointer-container"></div>
                    <section class="section">
                      <div class="pointer"></div>
                      <div class="abstract">
                        <p>Undocumented</p>

                      </div>
                      <div class="declaration">
                        <h4>Declaration</h4>
                        <div class="language">
                          <p class="aside-title">Swift</p>
                          <pre class="highlight swift"><code><span class="kd">public</span> <span class="k">var</span> <span class="nv">bitWidth</span><span class="p">:</span> <span class="kt">Int</span> <span class="p">{</span> <span class="k">get</span> <span class="p">}</span></code></pre>

                        </div>
                      </div>
                      <div class="slightly-smaller">
                        <a href="https://github.com/attaswift/tree/v5.2.1/Sources/Words and Bits.swift#L78-L81">Show on GitHub</a>
                      </div>
                    </section>
                  </div>
                </li>
                <li class="item">
                  <div>
                    <code>
                    <a name="/s:6BigIntAAV20trailingZeroBitCountSivp"></a>
                    <a name="//apple_ref/swift/Property/trailingZeroBitCount" class="dashAnchor"></a>
                    <a class="token" href="#/s:6BigIntAAV20trailingZeroBitCountSivp">trailingZeroBitCount</a>
                    </code>
                  </div>
                  <div class="height-container">
                    <div class="pointer-container"></div>
                    <section class="section">
                      <div class="pointer"></div>
                      <div class="abstract">
                        <p>Undocumented</p>

                      </div>
                      <div class="declaration">
                        <h4>Declaration</h4>
                        <div class="language">
                          <p class="aside-title">Swift</p>
                          <pre class="highlight swift"><code><span class="kd">public</span> <span class="k">var</span> <span class="nv">trailingZeroBitCount</span><span class="p">:</span> <span class="kt">Int</span> <span class="p">{</span> <span class="k">get</span> <span class="p">}</span></code></pre>

                        </div>
                      </div>
                      <div class="slightly-smaller">
                        <a href="https://github.com/attaswift/tree/v5.2.1/Sources/Words and Bits.swift#L83-L86">Show on GitHub</a>
                      </div>
                    </section>
                  </div>
                </li>
                <li class="item">
                  <div>
                    <code>
                    <a name="/s:Sz5WordsQa"></a>
                    <a name="//apple_ref/swift/Struct/Words" class="dashAnchor"></a>
                    <a class="token" href="#/s:Sz5WordsQa">Words</a>
                    </code>
                  </div>
                  <div class="height-container">
                    <div class="pointer-container"></div>
                    <section class="section">
                      <div class="pointer"></div>
                      <div class="abstract">
                        
                        <a href="../Structs/BigInt/Words.html" class="slightly-smaller">See more</a>
                      </div>
                      <div class="declaration">
                        <h4>Declaration</h4>
                        <div class="language">
                          <p class="aside-title">Swift</p>
                          <pre class="highlight swift"><code><span class="kd">public</span> <span class="kd">struct</span> <span class="kt">Words</span> <span class="p">:</span> <span class="kt">RandomAccessCollection</span></code></pre>

                        </div>
                      </div>
                      <div class="slightly-smaller">
                        <a href="https://github.com/attaswift/tree/v5.2.1/Sources/Words and Bits.swift#L139-L186">Show on GitHub</a>
                      </div>
                    </section>
                  </div>
                </li>
                <li class="item">
                  <div>
                    <code>
                    <a name="/s:6BigIntAAV5wordsAB5WordsVvp"></a>
                    <a name="//apple_ref/swift/Property/words" class="dashAnchor"></a>
                    <a class="token" href="#/s:6BigIntAAV5wordsAB5WordsVvp">words</a>
                    </code>
                  </div>
                  <div class="height-container">
                    <div class="pointer-container"></div>
                    <section class="section">
                      <div class="pointer"></div>
                      <div class="abstract">
                        <p>Undocumented</p>

                      </div>
                      <div class="declaration">
                        <h4>Declaration</h4>
                        <div class="language">
                          <p class="aside-title">Swift</p>
                          <pre class="highlight swift"><code><span class="kd">public</span> <span class="k">var</span> <span class="nv">words</span><span class="p">:</span> <span class="kt"><a href="../Structs/BigInt/Words.html">Words</a></span> <span class="p">{</span> <span class="k">get</span> <span class="p">}</span></code></pre>

                        </div>
                      </div>
                      <div class="slightly-smaller">
                        <a href="https://github.com/attaswift/tree/v5.2.1/Sources/Words and Bits.swift#L188-L190">Show on GitHub</a>
                      </div>
                    </section>
                  </div>
                </li>
                <li class="item">
                  <div>
                    <code>
                    <a name="/s:6BigIntAAV5wordsABx_tcSTRzSu7ElementRtzlufc"></a>
                    <a name="//apple_ref/swift/Method/init(words:)" class="dashAnchor"></a>
                    <a class="token" href="#/s:6BigIntAAV5wordsABx_tcSTRzSu7ElementRtzlufc">init(words:<wbr>)</a>
                    </code>
                  </div>
                  <div class="height-container">
                    <div class="pointer-container"></div>
                    <section class="section">
                      <div class="pointer"></div>
                      <div class="abstract">
                        <p>Undocumented</p>

                      </div>
                      <div class="declaration">
                        <h4>Declaration</h4>
                        <div class="language">
                          <p class="aside-title">Swift</p>
                          <pre class="highlight swift"><code><span class="kd">public</span> <span class="kd">init</span><span class="o">&lt;</span><span class="kt">S</span><span class="o">&gt;</span><span class="p">(</span><span class="nv">words</span><span class="p">:</span> <span class="kt">S</span><span class="p">)</span> <span class="k">where</span> <span class="kt">S</span> <span class="p">:</span> <span class="kt">Sequence</span><span class="p">,</span> <span class="kt">S</span><span class="o">.</span><span class="kt">Element</span> <span class="o">==</span> <span class="kt">BigInt</span><span class="o">.</span><span class="kt"><a href="../Structs/BigInt.html#/s:6BigIntAAV4Worda">Word</a></span></code></pre>

                        </div>
                      </div>
                      <div class="slightly-smaller">
                        <a href="https://github.com/attaswift/tree/v5.2.1/Sources/Words and Bits.swift#L192-L201">Show on GitHub</a>
                      </div>
                    </section>
                  </div>
                </li>
              </ul>
            </div>
          </div>
        </section>

      </article>
    </div>
    <section class="footer">
      <p>© 2020 <a class="link" href="https://twitter.com/lorentey" target="_blank" rel="external">Károly Lőrentey</a>. (Last updated: 2020-12-15)</p>
      <p>Generated by <a class="link" href="https://github.com/realm/jazzy" target="_blank" rel="external">jazzy ♪♫ v0.13.6</a>, a <a class="link" href="https://realm.io" target="_blank" rel="external">Realm</a> project.</p>
    </section>
  </body>
</div>
</html>
